Exchangeable measures for subshifts

Aaronson, J.; Nakada, H.; Sarig, O.

doi:10.1016/j.anihpb.2005.10.002

Aaronson, J. ; Nakada, H. ; Sarig, O.

Annales de l'I.H.P. Probabilités et statistiques, Tome 42 (2006) no. 6, pp. 727-751.

MR Zbl

DOI : 10.1016/j.anihpb.2005.10.002

@article{AIHPB_2006__42_6_727_0,
     author = {Aaronson, J. and Nakada, H. and Sarig, O.},
     title = {Exchangeable measures for subshifts},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {727--751},
     publisher = {Elsevier},
     volume = {42},
     number = {6},
     year = {2006},
     doi = {10.1016/j.anihpb.2005.10.002},
     mrnumber = {2269236},
     zbl = {1110.60025},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.anihpb.2005.10.002/}
}

TY  - JOUR
AU  - Aaronson, J.
AU  - Nakada, H.
AU  - Sarig, O.
TI  - Exchangeable measures for subshifts
JO  - Annales de l'I.H.P. Probabilités et statistiques
PY  - 2006
SP  - 727
EP  - 751
VL  - 42
IS  - 6
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.anihpb.2005.10.002/
DO  - 10.1016/j.anihpb.2005.10.002
LA  - en
ID  - AIHPB_2006__42_6_727_0
ER  -

%0 Journal Article
%A Aaronson, J.
%A Nakada, H.
%A Sarig, O.
%T Exchangeable measures for subshifts
%J Annales de l'I.H.P. Probabilités et statistiques
%D 2006
%P 727-751
%V 42
%N 6
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.anihpb.2005.10.002/
%R 10.1016/j.anihpb.2005.10.002
%G en
%F AIHPB_2006__42_6_727_0

Aaronson, J.; Nakada, H.; Sarig, O. Exchangeable measures for subshifts. Annales de l'I.H.P. Probabilités et statistiques, Tome 42 (2006) no. 6, pp. 727-751. doi : 10.1016/j.anihpb.2005.10.002. http://www.numdam.org/articles/10.1016/j.anihpb.2005.10.002/

Bibliographie
Cité par

[1] J. Aaronson, M. Denker, Group extensions of Gibbs-Markov maps, Probab. Theory Related Fields 123 (1) (2002) 38-40. | MR | Zbl

[2] J. Aaronson, M. Denker, M. Urbański, Ergodic theory for Markov fibred systems and parabolic rational maps, Trans. Amer. Math. Soc. 337 (2) (1993) 495-548. | MR | Zbl

[3] J. Aaronson, M. Denker, O. Sarig, R. Zweimüller, Aperiodicity of cocycles and conditional local limit theorems, Stoch. Dyn. 4 (1) (2004) 31-62. | MR | Zbl

[4] J. Aaronson, H. Nakada, O. Sarig, R. Solomyak, Invariant measures and asymptotics for some skew products, Israel J. Math. 128 (2002) 93-134. | MR | Zbl

[5] J. Aaronson, H. Nakada, O. Sarig, R. Solomyak, Corrections to: Invariant measures and asymptotics for some skew products, Israel J. Math. 138 (2003) 377-379. | MR | Zbl

[6] F. Blanchard, β-expansions and symbolic dynamics, Theoret. Comput. Sci. 65 (2) (1989) 131-141. | Zbl

[7] K.L. Chung, Markov Chains with Stationary Transition Probabilities, Springer, Heidelberg, 1960. | MR | Zbl

[8] P. Diaconis, D. Freedman, De Finetti's theorem for Markov chains, Ann. Probab. 8 (8) (1980) 115-130. | MR | Zbl

[9] E. Effros, Transformation groups and $C^{*}$ -algebras, Ann. of Math. (2) 81 (1965) 38-55. | Zbl

[10] J. Feldman, C.C. Moore, Ergodic equivalence relations, cohomology, and von Neumann algebras. I, Trans. Amer. Math. Soc. 234 (2) (1977) 289-324. | MR | Zbl

[11] L. Fuchs, Abelian Groups, Internat. Ser. Monogr. Pure Appl. Math., Pergamon Press, New York, 1960. | MR

[12] A.O. Gel'Fond, A common property of number systems, Izv. Akad. Nauk SSSR. Ser. Mat. 23 (1959) 809-814, (in Russian). | MR | Zbl

[13] J. Glimm, Locally compact transformation groups, Trans. Amer. Math. Soc. 101 (1961) 124-138. | MR | Zbl

[14] G. Greschonig, K. Schmidt, Ergodic decomposition of quasi-invariant probability measures, part 2, Colloq. Math. 84/85 (2000) 495-514. | EuDML | MR | Zbl

[15] L.A. Grigorenko, On the σ-algebra of symmetric events for a countable Markov chain, Theory Probab. Appl. 24 (1979) 199-204. | Zbl

[16] E. Hewitt, L.J. Savage, Symmetric measures on Cartesian products, Trans. Amer. Math. Soc. 80 (1955) 470-501. | MR | Zbl

[17] S. Ito, Y. Takahashi, Markov subshifts and realization of β-expansions, J. Math. Soc. Japan 26 (1974) 33-55. | Zbl

[18] A.N. Livšic, Certain properties of the homology of U-systems, Mat. Zametki 10 (1971) 555-564, English Transl. in, Math. Notes 10 (1971) 758-763. | MR | Zbl

[19] D. Maharam, Incompressible transformations, Fund. Math. 56 (1964) 35-50. | EuDML | MR | Zbl

[20] P.-A. Meyer, Probability and Potentials, Blaisdell Publishing Co, Ginn and Co, Waltham, MA, 1966. | MR | Zbl

[21] W. Parry, On the β-expansions of real numbers, Acta Math. Acad. Sci. Hungar. 11 (1960) 401-416. | Zbl

[22] W. Parry, K. Schmidt, Natural coefficients and invariants for Markov-shifts, Invent. Math. 76 (1) (1984) 15-32. | EuDML | MR | Zbl

[23] K. Petersen, K. Schmidt, Symmetric Gibbs measures, Trans. Amer. Math. Soc. 349 (1997) 2775-2811. | MR | Zbl

[24] A. Rényi, Representations for real numbers and their ergodic properties, Acta Math. Acad. Sci. Hungar. 8 (1957) 477-493. | MR | Zbl

[25] O. Sarig, Existence of Gibbs measures for countable Markov shifts, Proc. Amer. Math. Soc. 131 (6) (2003) 1751-1758. | MR | Zbl

[26] K. Schmidt, Infinite invariant measures on the circle, in: Convegno sulle Misure su Gruppi e su Spazi Vettoriali, Convegno sui Gruppi e Anelli Ordinati, INDAM, Rome, 1975, Symposia Mathematica, vol. XXI, Academic Press, London, 1977, pp. 37-43. | MR | Zbl

[27] F. Schweiger, Ergodic Theory of Fibred Systems and Metric Number Theory, Oxford Science Publications, The Clarendon Press, Oxford University Press, New York, 1995. | MR | Zbl

[28] M. Smorodinsky, β-automorphisms are Bernoulli shifts, Acta. Math. Acad. Sci. Hungar. 24 (1973) 273-278. | Zbl

[29] D. Vere-Jones, Ergodic properties of nonnegative matrices. I, Pacific J. Math. 22 (1967) 361-386. | MR | Zbl

[30] P. Walters, Equilibrium states for β-transformations and related transformations, Math. Z. 159 (1) (1978) 65-88. | EuDML | Zbl

Cité par Sources :