Determinantal probability measures
Publications Mathématiques de l'IHÉS, Tome 98 (2003), pp. 167-212.

Determinantal point processes have arisen in diverse settings in recent years and have been investigated intensively. We study basic combinatorial and probabilistic aspects in the discrete case. Our main results concern relationships with matroids, stochastic domination, negative association, completeness for infinite matroids, tail triviality, and a method for extension of results from orthogonal projections to positive contractions. We also present several new avenues for further investigation, involving Hilbert spaces, combinatorics, homology, and group representations, among other areas.

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Lyons, Russell. Determinantal probability measures. Publications Mathématiques de l'IHÉS, Tome 98 (2003), pp. 167-212. doi : 10.1007/s10240-003-0016-0. https://www.numdam.org/articles/10.1007/s10240-003-0016-0/

1. D. J. Aldous (1990), The random walk construction of uniform spanning trees and uniform labelled trees. SIAM J. Discrete Math., 3, 450-465. | MR | Zbl

2. N. Alon and J. H. Spencer (2001), The Probabilistic Method. Second edition. New York: John Wiley & Sons Inc. | MR | Zbl

3. I. Benjamini, R. Lyons, Y. Peres, and O. Schramm (1999), Group-invariant percolation on graphs. Geom. Funct. Anal., 9, 29-66. | MR | Zbl

4. I. Benjamini, R. Lyons, Y. Peres, and O. Schramm (2001), Uniform spanning forests. Ann. Probab., 29, 1-65. | MR | Zbl

5. J. Van Den Berg, and H. Kesten (1985), Inequalities with applications to percolation and reliability. J. Appl. Probab., 22, 556-569. | MR | Zbl

6. A. Beurling and P. Malliavin (1967), On the closure of characters and the zeros of entire functions. Acta Math., 118, 79-93. | MR | Zbl

7. A. Borodin (2000), Characters of symmetric groups, and correlation functions of point processes. Funkts. Anal. Prilozh., 34, 12-28, 96. English translation: Funct. Anal. Appl., 34(1), 10-23. | MR | Zbl

8. A. Borodin, A. Okounkov, and G. Olshanski (2000), Asymptotics of Plancherel measures for symmetric groups. J. Am. Math. Soc., 13, 481-515 (electronic). | MR | Zbl

9. A. Borodin and G. Olshanski (2000), Distributions on partitions, point processes, and the hypergeometric kernel. Comment. Math. Phys., 211, 335-358. | MR | Zbl

10. A. Borodin and G. Olshanski (2001), z-measures on partitions, Robinson-Schensted-Knuth correspondence, and β=2 random matrix ensembles. In P. Bleher and A. Its, eds., Random Matrix Models and Their Applications, vol. 40 of Math. Sci. Res. Inst. Publ., pp. 71-94. Cambridge: Cambridge Univ. Press. | Zbl

11. A. Borodin and G. Olshanski (2002), Harmonic analysis on the infinite-dimensional unitary group and determinantal point processes. Preprint. | MR | Zbl

12. J. Bourgain and L. Tzafriri (1987), Invertibility of “large” submatrices with applications to the geometry of Banach spaces and harmonic analysis. Isr. J. Math., 57, 137-224. | Zbl

13. A. Broder (1989), Generating random spanning trees. In 30th Annual Symposium on Foundations of Computer Science (Research Triangle Park, North Carolina), pp. 442-447. New York: IEEE.

14. R. L. Brooks, C. A. B. Smith, A. H. Stone, and W. T. Tutte (1940), The dissection of rectangles into squares. Duke Math. J., 7, 312-340. | MR | Zbl

15. R. M. Burton and R. Pemantle (1993), Local characteristics, entropy and limit theorems for spanning trees and domino tilings via transfer-impedances. Ann. Probab., 21, 1329-1371. | MR | Zbl

16. J. Cheeger and M. Gromov (1986), L2-cohomology and group cohomology. Topology, 25, 189-215. | MR | Zbl

17. Y. B. Choe, J. Oxley, A. Sokal, and D. Wagner (2003), Homogeneous multivariate polynomials with the half-plane property. Adv. Appl. Math. To appear. | MR | Zbl

18. J. B. Conrey (2003), The Riemann hypothesis. Notices Am. Math. Soc., 50, 341-353. | MR

19. J. B. Conway (1990), A Course in Functional Analysis. Second edition. New York: Springer. | MR | Zbl

20. J. P. Conze (1972/73), Entropie d'un groupe abélien de transformations. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 25, 11-30. | Zbl

21. D. J. Daley and D. Vere-Jones (1988), An Introduction to the Theory of Point Processes. New York: Springer. | MR | Zbl

22. P. Diaconis (2003), Patterns in eigenvalues: the 70th Josiah Willard Gibbs lecture. Bull. Am. Math. Soc., New Ser., 40, 155-178 (electronic). | MR

23. D. Dubhashi and D. Ranjan (1998), Balls and bins: a study in negative dependence. Random Struct. Algorithms, 13, 99-124. | MR | Zbl

24. F. J. Dyson (1962), Statistical theory of the energy levels of complex systems. III. J. Math. Phys., 3, 166-175. | MR | Zbl

25. T. Feder and M. Mihail (1992), Balanced matroids. In Proceedings of the Twenty-Fourth Annual ACM Symposium on Theory of Computing, pp. 26-38, New York. Association for Computing Machinery (ACM). Held in Victoria, BC, Canada.

26. R. M. Foster (1948), The average impedance of an electrical network. In Reissner Anniversary Volume, Contributions to Applied Mechanics, pp. 333-340. J. W. Edwards, Ann Arbor, Michigan. Edited by the Staff of the Department of Aeronautical Engineering and Applied Mechanics of the Polytechnic Institute of Brooklyn. | MR | Zbl

27. W. Fulton and J. Harris (1991), Representation Theory: A First Course. Readings in Mathematics. New York: Springer. | MR | Zbl

28. D. Gaboriau (2002), Invariants l2 de relations d'équivalence et de groupes. Publ. Math., Inst. Hautes Étud. Sci., 95, 93-150. | Numdam | Zbl

29. H. O. Georgii (1988), Gibbs Measures and Phase Transitions. Berlin-New York: Walter de Gruyter & Co. | MR | Zbl

30. O. Häggström (1995), Random-cluster measures and uniform spanning trees. Stochastic Processes Appl., 59, 267-275. | MR | Zbl

31. P. R. Halmos (1982), A Hilbert Space Problem Book. Second edition. Encycl. Math. Appl. 17, New York: Springer. | MR | Zbl

32. D. Heicklen and R. Lyons (2003), Change intolerance in spanning forests. J. Theor. Probab., 16, 47-58. | MR | Zbl

33. K. Johansson (2001), Discrete orthogonal polynomial ensembles and the Plancherel measure. Ann. Math. (2), 153, 259-296. | MR | Zbl

34. K. Johansson (2002), Non-intersecting paths, random tilings and random matrices. Probab. Theory Relat. Fields, 123, 225-280. | MR | Zbl

35. G. Kalai (1983), Enumeration of Q-acyclic simplicial complexes. Isr. J. Math., 45, 337-351. | MR | Zbl

36. Y. Katznelson and B. Weiss (1972), Commuting measure-preserving transformations. Isr. J. Math., 12, 161-173. | MR | Zbl

37. G. Kirchhoff (1847), Über die Auflösung der Gleichungen, auf welche man bei der Untersuchung der linearen Vertheilung galvanischer Ströme geführt wird. Ann. Phys. Chem., 72, 497-508.

38. R. Lyons (1998), A bird's-eye view of uniform spanning trees and forests. In D. Aldous and J. Propp, eds., Microsurveys in Discrete Probability, vol. 41 of DIMACS Series in Discrete Mathematics and Theoretical Computer Science, pp. 135-162. Providence, RI: Am. Math. Soc., Papers from the workshop held as part of the Dimacs Special Year on Discrete Probability in Princeton, NJ, June 2-6, 1997. | Zbl

39. R. Lyons (2000), Phase transitions on nonamenable graphs. J. Math. Phys., 41, 1099-1126. Probabilistic techniques in equilibrium and nonequilibrium statistical physics. | MR | Zbl

40. R. Lyons (2003), Random complexes and ℓ2-Betti numbers. In preparation.

41. R. Lyons, Y. Peres, and O. Schramm (2003), Minimal spanning forests. In preparation.

42. R. Lyons and J. E. Steif (2003), Stationary determinantal processes: Phase multiplicity, Bernoullicity, entropy, and domination. Duke Math. J. To appear. | MR | Zbl

43. O. Macchi (1975), The coincidence approach to stochastic point processes. Adv. Appl. Probab., 7, 83-122. | MR | Zbl

44. S. B. Maurer (1976), Matrix generalizations of some theorems on trees, cycles and cocycles in graphs. SIAM J. Appl. Math., 30, 143-148. | MR | Zbl

45. M. L. Mehta (1991), Random Matrices. Second edition. Boston, MA: Academic Press Inc. | MR | Zbl

46. B. Morris (2003), The components of the wired spanning forest are recurrent. Probab. Theory Related Fields, 125, 259-265. | MR | Zbl

47. C. M. Newman (1984), Asymptotic independence and limit theorems for positively and negatively dependent random variables. In Y. L. Tong, ed., Inequalities in Statistics and Probability, pp. 127-140. Hayward, CA: Inst. Math. Statist. Proceedings of the symposium held at the University of Nebraska, Lincoln, Neb., October 27-30, 1982. | MR

48. A. Okounkov (2001), Infinite wedge and random partitions. Sel. Math., New Ser., 7, 57-81. | MR | Zbl

49. A. Okounkov and N. Reshetikhin (2003), Correlation function of Schur process with application to local geometry of a random 3-dimensional Young diagram. J. Am. Math. Soc., 16, 581-603 (electronic). | MR | Zbl

50. D. S. Ornstein and B. Weiss (1987), Entropy and isomorphism theorems for actions of amenable groups. J. Anal. Math., 48, 1-141. | MR | Zbl

51. J. G. Oxley (1992), Matroid Theory. New York: Oxford University Press. | MR | Zbl

52. R. Pemantle (1991), Choosing a spanning tree for the integer lattice uniformly. Ann. Probab., 19, 1559-1574. | MR | Zbl

53. R. Pemantle (2000), Towards a theory of negative dependence. J. Math. Phys., 41, 1371-1390. Probabilistic techniques in equilibrium and nonequilibrium statistical physics. | MR | Zbl

54. J. G. Propp and D. B. Wilson (1998), How to get a perfectly random sample from a generic Markov chain and generate a random spanning tree of a directed graph. J. Algorithms, 27, 170-217. 7th Annual ACM-SIAM Symposium on Discrete Algorithms (Atlanta, GA, 1996). | MR | Zbl

55. R. Redheffer (1972), Two consequences of the Beurling-Malliavin theory. Proc. Am. Math. Soc., 36, 116-122. | MR | Zbl

56. R. M. Redheffer (1977), Completeness of sets of complex exponentials. Adv. Math., 24, 1-62. | MR | Zbl

57. K. Seip and A. M. Ulanovskii (1997), The Beurling-Malliavin density of a random sequence. Proc. Am. Math. Soc., 125, 1745-1749. | MR | Zbl

58. Q. M. Shao (2000), A comparison theorem on moment inequalities between negatively associated and independent random variables. J. Theor. Probab., 13, 343-356. | MR | Zbl

59. Q. M. Shao and C. Su (1999), The law of the iterated logarithm for negatively associated random variables. Stochastic Processes Appl., 83, 139-148. | MR | Zbl

60. T. Shirai and Y. Takahashi (2000), Fermion process and Fredholm determinant. In H. G. W. Begehr, R. P. Gilbert, and J. Kajiwara, eds., Proceedings of the Second ISAAC Congress, vol. 1, pp. 15-23. Kluwer Academic Publ. International Society for Analysis, Applications and Computation, vol. 7. | MR | Zbl

61. T. Shirai and Y. Takahashi (2002), Random point fields associated with certain Fredholm determinants I: fermion, Poisson and boson point processes. Preprint. | MR | Zbl

62. T. Shirai and Y. Takahashi (2003), Random point fields associated with certain Fredholm determinants II: fermion shifts and their ergodic and Gibbs properties. Ann. Probab., 31, 1533-1564. | MR | Zbl

63. T. Shirai and H. J. Yoo (2002), Glauber dynamics for fermion point processes. Nagoya Math. J., 168, 139-166. | MR | Zbl

64. A. Soshnikov (2000a), Determinantal random point fields. Usp. Mat. Nauk, 55, 107-160. | MR | Zbl

65. A. B. Soshnikov (2000b), Gaussian fluctuation for the number of particles in Airy, Bessel, sine, and other determinantal random point fields. J. Stat. Phys., 100, 491-522. | MR | Zbl

66. V. Strassen (1965), The existence of probability measures with given marginals. Ann. Math. Stat., 36, 423-439. | MR | Zbl

67. C. Thomassen (1990), Resistances and currents in infinite electrical networks. J. Combin. Theory, Ser. B, 49, 87-102. | MR | Zbl

68. J. P. Thouvenot (1972), Convergence en moyenne de l'information pour l'action de Z2. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 24, 135-137. | Zbl

69. A. M. Vershik and S. V. Kerov (1981), Asymptotic theory of the characters of a symmetric group. Funkts. Anal. i Prilozh., 15, 15-27, 96. English translation: Funct. Anal. Appl., 15(4), 246-255 (1982). | MR | Zbl

70. D. J. A. Welsh (1976), Matroid Theory. London: Academic Press [Harcourt Brace Jovanovich Publishers]. L. M. S. Monographs, No. 8. | MR | Zbl

71. N. White, ed. (1987), Combinatorial Geometries. Cambridge: Cambridge University Press. | MR | Zbl

72. H. Whitney (1935), On the abstract properties of linear dependence. Am. J. Math., 57, 509-533. | MR | Zbl

73. H. Whitney (1957), Geometric Integration Theory. Princeton, N.J.: Princeton University Press. | MR | Zbl

74. D. B. Wilson (1996), Generating random spanning trees more quickly than the cover time. In Proceedings of the Twenty-eighth Annual ACM Symposium on the Theory of Computing, pp. 296-303. New York: ACM. Held in Philadelphia, PA, May 22-24, 1996. | MR | Zbl

75. L. X. Zhang (2001), Strassen's law of the iterated logarithm for negatively associated random vectors. Stochastic Processes Appl., 95, 311-328. | Zbl

76. L. X. Zhang and J. Wen (2001), A weak convergence for negatively associated fields. Stat. Probab. Lett., 53, 259-267. | MR | Zbl

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  • Reddy, Tulasi Ram; Vadlamani, Sreekar; Yogeshwaran, D. Central Limit Theorem for Exponentially Quasi-local Statistics of Spin Models on Cayley Graphs, Journal of Statistical Physics, Volume 173 (2018) no. 3-4, p. 941 | DOI:10.1007/s10955-018-2026-9
  • Fan, Aihua; Fan, Shilei; Qiu, Yanqi Some properties of stationary determinantal point processes on Z, Journal of the London Mathematical Society, Volume 98 (2018) no. 3, p. 517 | DOI:10.1112/jlms.12145
  • Bufetov, Alexander I.; Qiu, Yanqi J-Hermitian determinantal point processes: balanced rigidity and balanced Palm equivalence, Mathematische Annalen, Volume 371 (2018) no. 1-2, p. 127 | DOI:10.1007/s00208-017-1627-y
  • Balzer, Laura B.; van der Laan, Mark J.; Petersen, Maya L. Data-Adaptive Estimation in Cluster Randomized Trials, Targeted Learning in Data Science (2018), p. 195 | DOI:10.1007/978-3-319-65304-4_13
  • Rose, Sherri; van der Laan, Mark J. Research Questions in Data Science, Targeted Learning in Data Science (2018), p. 3 | DOI:10.1007/978-3-319-65304-4_1
  • Chambaz, Antoine; Joly, Emilien; Mary, Xavier Targeted Learning Using Adaptive Survey Sampling, Targeted Learning in Data Science (2018), p. 541 | DOI:10.1007/978-3-319-65304-4_29
  • Bufetov, Alexander I. Quasi-symmetries of determinantal point processes, The Annals of Probability, Volume 46 (2018) no. 2 | DOI:10.1214/17-aop1198
  • Duits, Maurice On global fluctuations for non-colliding processes, The Annals of Probability, Volume 46 (2018) no. 3 | DOI:10.1214/17-aop1185
  • Bufetov, Alexander I.; Qiu, Yanqi Determinantal Point Processes Associated with Hilbert Spaces of Holomorphic Functions, Communications in Mathematical Physics, Volume 351 (2017) no. 1, p. 1 | DOI:10.1007/s00220-017-2840-y
  • Baraud, Yannick Estimation of the density of a determinantal process, Confluentes Mathematici, Volume 5 (2017) no. 1, p. 3 | DOI:10.5802/cml.1
  • Ghosh, Subhroshekhar; Peres, Yuval Rigidity and tolerance in point processes: Gaussian zeros and Ginibre eigenvalues, Duke Mathematical Journal, Volume 166 (2017) no. 10 | DOI:10.1215/00127094-2017-0002
  • Bufetov, Alexander Igorevich; Shirai, Tomoyuki Quasi-symmetries and rigidity for determinantal point processes associated with de Branges spaces, Proceedings of the Japan Academy, Series A, Mathematical Sciences, Volume 93 (2017) no. 1 | DOI:10.3792/pjaa.93.1
  • Bufetov, Alexander I. A palm hierarchy for determinantal point processes with the Bessel kernel, Proceedings of the Steklov Institute of Mathematics, Volume 297 (2017) no. 1, p. 90 | DOI:10.1134/s0081543817040058
  • Bufetov, Alexander I. Rigidity of determinantal point processes with the Airy, the Bessel and the Gamma kernel, Bulletin of Mathematical Sciences, Volume 6 (2016) no. 1, p. 163 | DOI:10.1007/s13373-015-0080-z
  • Breuer, Jonathan; Duits, Maurice Universality of Mesoscopic Fluctuations for Orthogonal Polynomial Ensembles, Communications in Mathematical Physics, Volume 342 (2016) no. 2, p. 491 | DOI:10.1007/s00220-015-2514-6
  • LYONS, RUSSELL; THOM, ANDREAS Invariant coupling of determinantal measures on sofic groups, Ergodic Theory and Dynamical Systems, Volume 36 (2016) no. 2, p. 574 | DOI:10.1017/etds.2014.70
  • Kook, Woong; Lee, Kang-Ju A formula for simplicial tree-numbers of matroid complexes, European Journal of Combinatorics, Volume 53 (2016), p. 59 | DOI:10.1016/j.ejc.2015.11.001
  • Bufetov, A I Infinite determinantal measures and the ergodic decomposition of infinite Pickrell measures. II. Convergence of infinite determinantal measures, Izvestiya: Mathematics, Volume 80 (2016) no. 2, p. 299 | DOI:10.1070/im8384
  • Breuer, Jonathan; Duits, Maurice Central limit theorems for biorthogonal ensembles and asymptotics of recurrence coefficients, Journal of the American Mathematical Society, Volume 30 (2016) no. 1, p. 27 | DOI:10.1090/jams/854
  • Nikolov, Aleksandar; Singh, Mohit, Proceedings of the forty-eighth annual ACM symposium on Theory of Computing (2016), p. 192 | DOI:10.1145/2897518.2897649
  • Ghosh, Subhroshekhar; Krishnapur, Manjunath; Peres, Yuval Continuum percolation for Gaussian zeroes and Ginibre eigenvalues, The Annals of Probability, Volume 44 (2016) no. 5 | DOI:10.1214/15-aop1051
  • Bufetov, Aleksandr Igorevich Бесконечные детерминантные меры и эргодическое разложение бесконечных мер Пикрелла. II. Сходимость бесконечных детерминантных мер, Известия Российской академии наук. Серия математическая, Volume 80 (2016) no. 2, p. 16 | DOI:10.4213/im8384
  • Bufetov, Alexander I.; Qiu, Yanqi Equivalence of Palm measures for determinantal point processes associated with Hilbert spaces of holomorphic functions, Comptes Rendus. Mathématique, Volume 353 (2015) no. 6, p. 551 | DOI:10.1016/j.crma.2015.03.018
  • Bufetov, A I Infinite determinantal measures and the ergodic decomposition of infinite Pickrell measures. I. Construction of infinite determinantal measures, Izvestiya: Mathematics, Volume 79 (2015) no. 6, p. 1111 | DOI:10.1070/im2015v079n06abeh002775
  • Ghosh, Subhroshekhar Determinantal processes and completeness of random exponentials: the critical case, Probability Theory and Related Fields, Volume 163 (2015) no. 3-4, p. 643 | DOI:10.1007/s00440-014-0601-9
  • Bufetov, Aleksandr Igorevich Бесконечные детерминантные меры и эргодическое разложение бесконечных мер Пикрелла. I. Построение бесконечных детерминантных мер, Известия Российской академии наук. Серия математическая, Volume 79 (2015) no. 6, p. 18 | DOI:10.4213/im8383
  • Błaszczyszyn, Bartłomiej; Yogeshwaran, D. On Comparison of Clustering Properties of Point Processes, Advances in Applied Probability, Volume 46 (2014) no. 1, p. 1 | DOI:10.1239/aap/1396360100
  • Breuer, Jonathan; Duits, Maurice The Nevai condition and a local law of large numbers for orthogonal polynomial ensembles, Advances in Mathematics, Volume 265 (2014), p. 441 | DOI:10.1016/j.aim.2014.07.026
  • PEMANTLE, ROBIN; PERES, YUVAL Concentration of Lipschitz Functionals of Determinantal and Other Strong Rayleigh Measures, Combinatorics, Probability and Computing, Volume 23 (2014) no. 1, p. 140 | DOI:10.1017/s0963548313000345
  • Duits, Maurice Painlevé Kernels in Hermitian Matrix Models, Constructive Approximation, Volume 39 (2014) no. 1, p. 173 | DOI:10.1007/s00365-013-9201-7
  • Pendavingh, R.A.; van Zwam, S.H.M. Skew partial fields, multilinear representations of matroids, and a matrix tree theorem, Advances in Applied Mathematics, Volume 50 (2013) no. 1, p. 201 | DOI:10.1016/j.aam.2011.08.003
  • Borodin, Alexei; Serfaty, Sylvia Renormalized Energy Concentration in Random Matrices, Communications in Mathematical Physics, Volume 320 (2013) no. 1, p. 199 | DOI:10.1007/s00220-013-1716-z
  • Duits, Maurice Gaussian Free Field in an Interlacing Particle System with Two Jump Rates, Communications on Pure and Applied Mathematics, Volume 66 (2013) no. 4, p. 600 | DOI:10.1002/cpa.21419
  • Duits, Maurice; Geudens, Dries A critical phenomenon in the two-matrix model in the quartic/quadratic case, Duke Mathematical Journal, Volume 162 (2013) no. 8 | DOI:10.1215/00127094-2208757
  • Merkl, Franz; Rolles, Silke Perturbation analysis of the van den Berg Kesten inequality for determinantal probability measures, Electronic Journal of Probability, Volume 18 (2013) no. none | DOI:10.1214/ejp.v18-2339
  • Bufetov, Alexander I. Infinite determinantal measures, Electronic Research Announcements in Mathematical Sciences, Volume 20 (2013) no. 0, p. 12 | DOI:10.3934/era.2013.20.12
  • Tao, Terence The asymptotic distribution of a single eigenvalue gap of a Wigner matrix, Probability Theory and Related Fields, Volume 157 (2013) no. 1-2, p. 81 | DOI:10.1007/s00440-012-0450-3
  • BERTOLA, M.; CAFASSO, M. THE GAP PROBABILITIES OF THE TACNODE, PEARCEY AND AIRY POINT PROCESSES, THEIR MUTUAL RELATIONSHIP AND EVALUATION, Random Matrices: Theory and Applications, Volume 02 (2013) no. 02, p. 1350003 | DOI:10.1142/s2010326313500032
  • Adler, Mark; Ferrari, Patrik L.; van Moerbeke, Pierre Nonintersecting random walks in the neighborhood of a symmetric tacnode, The Annals of Probability, Volume 41 (2013) no. 4 | DOI:10.1214/11-aop726
  • Ben Arous, Gérard; Bourgade, Paul Extreme gaps between eigenvalues of random matrices, The Annals of Probability, Volume 41 (2013) no. 4 | DOI:10.1214/11-aop710
  • Breuer, Jonathan; Duits, Maurice Nonintersecting paths with a staircase initial condition, Electronic Journal of Probability, Volume 17 (2012) no. none | DOI:10.1214/ejp.v17-1902
  • Ferrari, Patrik; Vető, Bálint Non-colliding Brownian bridges and the asymmetric tacnode process, Electronic Journal of Probability, Volume 17 (2012) no. none | DOI:10.1214/ejp.v17-1811
  • Eisenbaum, Nathalie Stochastic order for alpha-permanental point processes, Stochastic Processes and their Applications, Volume 122 (2012) no. 3, p. 952 | DOI:10.1016/j.spa.2011.11.006
  • Borodin, Alexei; Duits, Maurice Limits of determinantal processes near a tacnode, Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, Volume 47 (2011) no. 1 | DOI:10.1214/10-aihp373
  • Merkl, Franz; Rolles, Silke Correlation Inequalities for Edge-Reinforced Random Walk, Electronic Communications in Probability, Volume 16 (2011) no. none | DOI:10.1214/ecp.v16-1683
  • Cifarelli, D.M.; Fortini, S. Recursive equations for the predictive distributions of some determinantal processes, Statistics Probability Letters, Volume 81 (2011) no. 1, p. 8 | DOI:10.1016/j.spl.2010.09.012
  • Deshpande, Amit; Rademacher, Luis, 2010 IEEE 51st Annual Symposium on Foundations of Computer Science (2010), p. 329 | DOI:10.1109/focs.2010.38
  • Vandenberg-Rodes, Alexander A limit theorem for particle current in the symmetric exclusion process, Electronic Communications in Probability, Volume 15 (2010) no. none | DOI:10.1214/ecp.v15-1550
  • Goldman, André The Palm measure and the Voronoi tessellation for the Ginibre process, The Annals of Applied Probability, Volume 20 (2010) no. 1 | DOI:10.1214/09-aap620
  • Adler, Mark; Ferrari, Patrik L.; van Moerbeke, Pierre Airy processes with wanderers and new universality classes, The Annals of Probability, Volume 38 (2010) no. 2 | DOI:10.1214/09-aop493
  • CHAE, Myeongju; YOO, Hyun Jae Glauber and Kawasaki Dynamics for Determinantal Point Processes in Discrete Spaces, Interdisciplinary Information Sciences, Volume 15 (2009) no. 3, p. 377 | DOI:10.4036/iis.2009.377
  • LYONS, RUSSELL RANDOM COMPLEXES AND ℓ2-BETTI NUMBERS, Journal of Topology and Analysis, Volume 01 (2009) no. 02, p. 153 | DOI:10.1142/s1793525309000072
  • Evans, Steven N.; Gottlieb, Alex Hyperdeterminantal point processes, Metrika, Volume 69 (2009) no. 2-3, p. 85 | DOI:10.1007/s00184-008-0209-0
  • Borodin, Alexei Loop-free Markov chains as determinantal point processes, Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, Volume 44 (2008) no. 1 | DOI:10.1214/07-aihp115
  • Borodin, Alexei; Ferrari, Patrik Large time asymptotics of growth models on space-like paths I: PushASEP, Electronic Journal of Probability, Volume 13 (2008) no. none | DOI:10.1214/ejp.v13-541
  • Borcea, Julius; Brändén, Petter; Liggett, Thomas Negative dependence and the geometry of polynomials, Journal of the American Mathematical Society, Volume 22 (2008) no. 2, p. 521 | DOI:10.1090/s0894-0347-08-00618-8
  • Jorgensen, Palle E. T.; Kornelson, Keri A.; Shuman, Karen L. Affine Systems: Asymptotics at Infinity for Fractal Measures, Acta Applicandae Mathematicae, Volume 98 (2007) no. 3, p. 181 | DOI:10.1007/s10440-007-9156-4
  • Rider, Brian; Virag, Balint Complex Determinantal Processes and H1 Noise, Electronic Journal of Probability, Volume 12 (2007) no. none | DOI:10.1214/ejp.v12-446
  • Borodin, Alexei; Olshanski, Grigori Asymptotics of Plancherel-type random partitions, Journal of Algebra, Volume 313 (2007) no. 1, p. 40 | DOI:10.1016/j.jalgebra.2006.10.039
  • Yoo, Hyun Jae A Variational Principle in the Dual Pair of Reproducing Kernel Hilbert Spaces and an Application, Journal of Statistical Physics, Volume 126 (2007) no. 2, p. 325 | DOI:10.1007/s10955-006-9258-9
  • Borodin, Alexei; Ferrari, Patrik L.; Prähofer, Michael; Sasamoto, Tomohiro Fluctuation Properties of the TASEP with Periodic Initial Configuration, Journal of Statistical Physics, Volume 129 (2007) no. 5-6, p. 1055 | DOI:10.1007/s10955-007-9383-0
  • Soshnikov, A. Determinantal Random Fields, Encyclopedia of Mathematical Physics (2006), p. 47 | DOI:10.1016/b0-12-512666-2/00431-4
  • Klich, Israel Lower entropy bounds and particle number fluctuations in a Fermi sea, Journal of Physics A: Mathematical and General, Volume 39 (2006) no. 4, p. L85 | DOI:10.1088/0305-4470/39/4/l02
  • Yoo, Hyun Jae Gibbsianness of fermion random point fields, Mathematische Zeitschrift, Volume 252 (2006) no. 1, p. 27 | DOI:10.1007/s00209-005-0843-4
  • Jae Yoo, Hyun Dirichlet forms and diffusion processes for fermion random point fields, Journal of Functional Analysis, Volume 219 (2005) no. 1, p. 143 | DOI:10.1016/j.jfa.2004.03.006
  • Georgii, Hans-Otto; Yoo, Hyun Jae Conditional Intensity and Gibbsianness of Determinantal Point Processes, Journal of Statistical Physics, Volume 118 (2005) no. 1-2, p. 55 | DOI:10.1007/s10955-004-8777-5
  • Broman, Erik I. One-dependent trigonometric determinantal processes are two-block-factors, The Annals of Probability, Volume 33 (2005) no. 2 | DOI:10.1214/009117904000000595
  • Soshnikov, Alexander Janossy Densities of Coupled Random Matrices, Communications in Mathematical Physics, Volume 251 (2004) no. 3, p. 447 | DOI:10.1007/s00220-004-1177-5
  • Lyons, Russell; Steif, Jeffrey E. Stationary determinantal processes: Phase multiplicity, Bernoullicity, entropy, and domination, Duke Mathematical Journal, Volume 120 (2003) no. 3 | DOI:10.1215/s0012-7094-03-12032-3

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