Non-intersecting, simple, symmetric \- random walks and the extended Hahn kernel
[Marches aléatoires simples, symétriques et qui ne s'intersectent pas et le noyau de Hahn étendu]
Johansson, Kurt1
1 Royal Institute of Technology, department of mathematics, 100 44 Stockholm (Suède)
Annales de l'Institut Fourier, Tome 55 (2005) no. 6, pp. 2129-2145.

Nous montrons en utilisant des chemins qui ne s'intersectent pas qu'un pavage rhombique d'un hexagone, ou une partition planaire en boîtes, est décrit par un point processus ponctuel déterminentiel, donné par un noyau de Hahn étendu.

We show using non-intersecting paths, that a random rhombus tiling of a hexagon, or a boxed planar partition, is described by a determinantal point process given by an extended Hahn kernel.

DOI : 10.5802/aif.2155
Classification : 60K35, 15A32
Keywords: Non-intersecting paths, Dysons's Brownian motion, planar partitions, random tiling, determintal process
Mot clés : chemins qui ne s'intersectent pas, mouvement brownien de Dyson, partitions planaires, pavages aléatoires, processus déterminentiels
Johansson, Kurt 1

1 Royal Institute of Technology, department of mathematics, 100 44 Stockholm (Suède) 
@article{AIF_2005__55_6_2129_0,
     author = {Johansson, Kurt},
     title = {Non-intersecting, simple, symmetric \- random walks and the extended {Hahn} kernel},
     journal = {Annales de l'Institut Fourier},
     pages = {2129--2145},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {55},
     number = {6},
     year = {2005},
     doi = {10.5802/aif.2155},
     mrnumber = {2187949},
     zbl = {1083.60079},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/aif.2155/}
}
TY  - JOUR
AU  - Johansson, Kurt
TI  - Non-intersecting, simple, symmetric \- random walks and the extended Hahn kernel
JO  - Annales de l'Institut Fourier
PY  - 2005
SP  - 2129
EP  - 2145
VL  - 55
IS  - 6
PB  - Association des Annales de l’institut Fourier
UR  - http://www.numdam.org/articles/10.5802/aif.2155/
DO  - 10.5802/aif.2155
LA  - en
ID  - AIF_2005__55_6_2129_0
ER  - 
%0 Journal Article
%A Johansson, Kurt
%T Non-intersecting, simple, symmetric \- random walks and the extended Hahn kernel
%J Annales de l'Institut Fourier
%D 2005
%P 2129-2145
%V 55
%N 6
%I Association des Annales de l’institut Fourier
%U http://www.numdam.org/articles/10.5802/aif.2155/
%R 10.5802/aif.2155
%G en
%F AIF_2005__55_6_2129_0
Johansson, Kurt. Non-intersecting, simple, symmetric \- random walks and the extended Hahn kernel. Annales de l'Institut Fourier, Tome 55 (2005) no. 6, pp. 2129-2145. doi : 10.5802/aif.2155. http://www.numdam.org/articles/10.5802/aif.2155/

[1] G.E. Andrews; R. Askey; R. Roy Special Functions, Encyclopedia of Mathematics and its applications, 71, Cambridge University Press, Cambridge, 1999 | MR | Zbl

[2] J. Baik; T. Kriecherbauer; K.D.T.-R MacLaughlin; P. Miller Uniform asymptotics for polynomials orthogonal with respect to a general class of discrete weights and universality results for associated ensembles (math.CA/0310278, http://arxiv.org/abs/math.CA/0310278)

[3] H. Cohn; M. Larsen; J. Propp The shape of a typical boxed plane partition, New York J. of Math., Volume 4 (1998), pp. 137-165 | MR | Zbl

[4] F. J. Dyson A Brownian-Motion Model for the eigenvalues of a Random Matrix, J. Math. Phys., Volume 3 (1962), pp. 1191-1198 | DOI | MR | Zbl

[5] B. Eynard; M. L. Mehta Matrices coupled in a chain I: Eigenvalue correlations, J. of Phys. A, Volume 31 (1998), pp. 4449-4456 | DOI | MR | Zbl

[6] P. L. Ferrari; H. Spohn Step fluctuations for a faceted crystal, J. Stat. Phys., Volume 113 (2003), pp. 1-46 | DOI | MR | Zbl

[7] P. J. Forrester; T. Nagao; G. Honner Correlations for the orthogonal-unitary and symplectic-unitary transitions at the soft and hard edges, Nucl. Phys. B, Volume 553 (1999), pp. 601-643 | DOI | MR | Zbl

[8] K. Holmaker On a discrete Rodrigues' formula and a second class of orthogonal Hahn polynomials (Preprint, Department of Mathematics, Chalmers University of Technology, N° 1977-12)

[9] K. Johansson Discrete orthogonal polynomial ensembles and the Plancherel measure, Annals of Math., Volume 153 (2001), pp. 259-296 | DOI | MR | Zbl

[10] K. Johansson Non-intersecting paths, random tilings and random matrices, Probab.Theory Relat. Fields, Volume 123 (2002), pp. 225-280 | DOI | MR | Zbl

[11] K. Johansson Discrete polynuclear growth and determinantal processes, Commun. Math. Phys., Volume 242 (2003), pp. 277-329 | MR | Zbl

[12] K. Johansson The Arctic circle and the Airy process (math.PR/0306216, to appear in Ann. Probab., http://arxiv.org/abs/math.PR/0306216) | MR | Zbl

[13] M. Katori; H. Tanemura Scaling limit of vicious walks and two-matrix model, Phys. Rev. E (2002)

[14] R. Kenyon Local statistics of lattice dimers, Ann. Inst. H. Poincaré, Probabilités et Statistiques, Volume 33 (1997), pp. 591-618 | DOI | Numdam | MR | Zbl

[15] M. L. Mehta Random Matrices, 2nd ed., Academic Press, San Diego, 1991 | MR | Zbl

[16] A. F. Nikiforov; S. K. Suslov; V. B. Uvarov Classical Orthogonal Polynomials of a Discrete Variable, Springer Series in Computational Physics, Berlin Heidelberg, Berlin Heidelberg, 1991 | MR | Zbl

[17] M. Prähofer; H. Spohn Scale invariance of the PNG droplet and the Airy process, J. Stat. Phys., Volume 108 (2002), pp. 1076-1106 | MR | Zbl

[18] R. P. Stanley Enumerative Combinatorics, Cambridge University Press, Volume 2 (1999) | Zbl

[19] J. R. Stembridge Nonintersecting Paths, Pfaffians, and Plane Partitions, Adv. in Math., Volume 83 (1990), pp. 96-131 | DOI | MR | Zbl

Cité par Sources :