Exponential Distribution for the Occurrence of Rare Patterns in Gibbsian Random Fields

Communications in Mathematical Physics

Volumn 246, Issue 2, 2004, Pages 269-294

  Abadi, M ^a   Chazottes, J R ^b   Redig, F ^c   Verbitskiy, E ^d  

^a UNIVERSITY OF SÃO PAULO   (Brazil)

^b CENTRE DE PHYSIQUE THÉORIQUE   (France)

^c EINDHOVEN UNIVERSITY OF TECHNOLOGY   (Netherlands)

^d PHILIPS RESEARCH LABORATORIES   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 2142684462     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00220-004-1041-7     Document Type: Article

References (29)

1. Abadi, M.: Exponential approximation for hitting times in mixing processes. Math. Phys. Electron. J. 7 (2001)
2. Abadi, M., Galves, A.: Inequalities for the occurrence of rare events in mixing processes. The state of the art. In: 'Inhomogeneous random systems' (Cergy-Pontoise, 2000), Markov Process. Related Fields 7(1), 97-112 (2001)
3. Asselah, A., Dai Pra, P.: Sharp estimates for the occurrence time of rare events for symmetric simple exclusion. Stochastic Process. Appl. 71(2), 259-273 (1997)
4. Asselah, A., Dai Pra, P.: Occurrence of rare events in ergodic interacting spin systems. Ann. Inst. H. Poincaré Probab. Statist. 33(6), 727-751 (1997)
5. Bowen, R.: Equilibrium states and the ergodic theory of Anosov diffeomorphisms. Lecture Notes in Math. 470, Berlin-Heidelberg-New York: Springer, 1975
6. Bryc, W.: A remark on the connection between the large deviation principle and the central limit theorem. Statist. & Probab. Lett. 18, 253-256 (1993)
7. Chazottes, J.-R.: Dimensions and waiting time for Gibbs measures. J. Stat. Phys. 98(3/4), 305-320 (2000)
8. Chi, Z.: The first-order asymptotic of waiting times with distortion between stationary processes. IEEE Trans. Inform. Theory 47(1), 338-347 (2001)
9. Collet, P., Galves, A., Schmitt, B.: Fluctuations of repetition times for gibbsian sources. Nonlinearity 12, 1225-1237 (1999)
10. d. CRAS, t. 303(11), 511-513 (1986)
11. Dembo, A., Kontoyiannis, I.: Source coding, large deviations and approximate pattern matching. IEEE Trans. Inf. Theory 48(6), 1590-1615 (2002)
12. Dembo, A., Zeitouni, O.: Large Deviations Techniques & Applications. Applic. Math. 38, Berlin-Heidelberg-New York: Springer, 1998
13. Dobrushin, R.L., Shlosman, S.B.: Completely analytical interactions: constructive description. J. Stat. Phys. 46(5-6), 983-1014 (1987)
14. Ellis, R.S.: Entropy, large deviations, and statistical mechanics. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 271, New York: Springer-Verlag, 1985
15. Daniels, H.A.M., van Enter, A.C.D.: Differentiability properties of the pressure in lattice systems. Commun. Math. Phys. 71(1), 65-76 (1980)
16. Georgii, H.-O.: Gibbs Measures and Phase Transitions. Berlin: Walter de Gruyter & Co., 1988
17. Guyon, X.: Random Fields on a Network. Modeling, Statistics and Applications. New York-Berlin: Springer Verlag, 1995
18. Haydn, N., Luévano, J., Mantica, G., Vaienti, S.: Multifractal Properties of Return Time Statistics. Phys.Rev. Lett. 88(22), (2002)
19. Krengel, U.: Ergodic theorems, de Gruyter Studies in Mathematics 6, Berlin: Walter de Gruyter & Co., 1985
20. Föllmer, H.: On entropy and information gain in random fields. Z. Wahrsch. Theorie Verw. Gebiete 26, 207-217 (1973)
21. Martinelli, F.: An elementary approach to finite size conditions for the exponential decay of covariances in lattice spin models. In: On Dobrushin's way. From probability theory to statistical physics, Am. Math. Soc. Transl. Ser. 2, 198, Providence, RI: Am. Math. Soc., 2000, pp. 169-181
22. Olla, S.: Large deviations for Gibbs random fields. Prob. Th. Rel. Fields 77, 343-357 (1988)
23. Omstein, D., Weiss, B.: Entropy and recurrence rates for stationary random fields. Special issue on Shannon theory: perspective, trends, and applications. IEEE Trans. Inform. Theory 48(6), 1694-1697 (2002)
24. Plachky, D., Steinebach, J.A.: A theorem about probabilities of large deviations with an application to queuing theory. Periodica Math. Hungar. 6, 343-345 (1975)
25. Ruelle, D.: Thermodynamic formalism. The mathematical structures of classical equilibrium statistical mechanics. Encyclopdia of Mathematics and its Applications 5. Reading, Mass.: Addison-Wesley Publishing Co., 1978
26. Shields, P.C.: The ergodic theory of discrete sample paths. Providence, RI: AMS, 1996
27. Simon, B.: The statistical mechanics of lattice gases. Vol. I. Princeton Series in Physics. Princeton, NJ: Princeton University Press, 1993
28. 2. Z. Wahrsch. Theorie Verw. Gebiete 24, 135-137 (1972)
29. Wyner, A.J.: More on recurrence and waiting times. Ann. Appl. Probab. 9(3), 780-796 (1999)