Ferrari, P. A.; Galves, A.; Liggett, T. M.
Exponential waiting time for filling a large interval in the symmetric simple exclusion process
Annales de l'I.H.P. Probabilités et statistiques, Tome 31 (1995) no. 1 , p. 155-175
Zbl 0819.60095 | MR 1340035 | 2 citations dans Numdam
URL stable : http://www.numdam.org/item?id=AIHPB_1995__31_1_155_0

Bibliographie

D.J. Aldous, Markov chains with almost exponential hitting times. Stochastic Process. Appl., Vol. 13, 1982, pp. 305-310. MR 671039 | Zbl 0491.60077

D.J. Aldous, Probability Approximations via the Poisson Clumping Heuristics. Springer Verlag, 1989. MR 969362 | Zbl 0679.60013

D.J. Aldous and M. Brown, Inequalities for rare events in time-reversible Markov chains I in M. Shaked and Y. L. Tong, Stochastic Inequalities IMS Lecture Notes, Vol. 22, 1992, pp. 1-16. MR 1228050

D.J. Aldous and M. Brown, Inequalities for rare events in time-reversible Markov chains II. Stochastic Processes Appl., Vol. 44, 1993, pp. 15-25. MR 1198660 | Zbl 0812.60054

R. Arratia and S. Tavare, Review of Probability Approximations via the Poisson Clumping Heuristic by D. Aldous and Poisson Approximations by A. D. Barbour, L. Holst and S. Janson, Ann. Probab., Vol. 21, 1993, pp. 2269-2279.

V. Belitsky, An upper bound of density for two-particle annihilating exclusion. J. Stat. Phys., Vol. 73, No.3/4, 1993, pp. 671-694. MR 1251659 | Zbl 1102.60322

V. Belitsky, Asymptotic behavior of density for two-particle annihilating exclusion. Preprint, 1994. MR 1315236

R. Bellman and T.E. Harris, Recurrence times for the Ehrenfest model. Pacific J. Math., Vol. 1, 1951, p. 179. MR 45323 | Zbl 0045.07802

M. Cassandro, A. Galves, E. Olivieri and M.E. Vares, Metastable behavior of stochastic dynamics: a pathwise approach J. Stat. Phys., Vol. 35, 1984, pp. 603-633. MR 749840 | Zbl 0591.60080

R. Cogburn, On the distribution of first passage and return times for small sets. Ann. Probab., Vol. 13, 1985, pp. 1219-1223. MR 806219 | Zbl 0591.60063

P. Collet, A. Galves and B. Schmitt, Unpredictability of the occurrence time of a long laminar period in a model of temporal intermittency. Ann. Inst. H. Poincaré, Section A, Vol. 57, 3, 1992, pp. 319-331. Numdam | MR 1185337 | Zbl 0756.60022

P.A. Ferrari, A. Galves and C. Landim, Exponential waiting time for a big gap in a one dimensional zero range process. Ann. Probab., Vol. 22, 1, 1994, pp. 284-288. MR 1258878 | Zbl 0793.60108

A. Galves, F. Martinelli and E. Olivieri, Large-density fluctuations for the one-dimensional supercritical contact process J. Stat. Phys., Vol. 55, 1989, pp. 639-648. MR 1003532 | Zbl 0713.60109

T.E. Harris, First passage and recurrence distributions. Trans. Amer. Math. Soc., Vol. 73, 1953, pp. 471-486. MR 52057 | Zbl 0048.36301

T.E. Harris, Additive set valued Markov processes and graphical methods. Ann. Probab., Vol. 6, 1978, pp. 355-378. MR 488377 | Zbl 0378.60106

C. Kipnis and C. Newman, The metastable behavior of infrequently observed, weakly random, one-dimensional diffusion processes. SIAM J. Appl. Math., Vol. 45, 1985, p. 972. MR 813459 | Zbl 0592.60063

D.V. Korolyuk and D. S. SIL'VESTROV, Entry times into asymptotically receding domains for ergodic Markov chains. Theory Prob. Appl., Vol. 19, 1984, pp. 432-442. Zbl 0533.60079

J.L. Lebowitz, R.H. Schonmann, On the asymptotics of occurrence times of rare events for stochastic spin systems. J. Stat. Phys., Vol. 48, 1987, pp. 727-751. MR 914904 | Zbl 01397656

T.M. Liggett, Interacting Particle Systems. Springer, Berlin, 1985. MR 776231 | Zbl 0559.60078

S.L. Lu and H-T. Yau, Spectral gap and logarithmic Sobolev inequality for Kawasaki and Glauber dynamics. Commun. Math. Phys., Vol. 156, 1993, pp. 399-433. MR 1233852 | Zbl 0779.60078

R. Schonmann, An approach to characterize metastability and critical droplets in stochastic Ising models. Ann. Inst. H. Poincaré, Section A, Vol. 55, 1991, pp. 591-600. Numdam | MR 1139535 | Zbl 0741.60103

F. Spitzer, Interaction of Markov processes. Adv. Math., Vol. 5, 1970, pp. 246-290. MR 268959 | Zbl 0312.60060