Occurrence of rare events in ergodic interacting spin systems

Amine Asselah; Paolo Dai Pra

Annales de l'I.H.P. Probabilités et statistiques (1997)

  • Volume: 33, Issue: 6, page 727-751
  • ISSN: 0246-0203

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Asselah, Amine, and Dai Pra, Paolo. "Occurrence of rare events in ergodic interacting spin systems." Annales de l'I.H.P. Probabilités et statistiques 33.6 (1997): 727-751. <http://eudml.org/doc/77588>.

@article{Asselah1997,
author = {Asselah, Amine, Dai Pra, Paolo},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {interacting spin systems; large deviations},
language = {eng},
number = {6},
pages = {727-751},
publisher = {Gauthier-Villars},
title = {Occurrence of rare events in ergodic interacting spin systems},
url = {http://eudml.org/doc/77588},
volume = {33},
year = {1997},
}

TY - JOUR
AU - Asselah, Amine
AU - Dai Pra, Paolo
TI - Occurrence of rare events in ergodic interacting spin systems
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 1997
PB - Gauthier-Villars
VL - 33
IS - 6
SP - 727
EP - 751
LA - eng
KW - interacting spin systems; large deviations
UR - http://eudml.org/doc/77588
ER -

References

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  1. [1] A. Asselah and G. Giacomin, in preparation. 
  2. [2] F. Comets, Nucleation for a long range magnetic model, Ann. Inst. H. Poincaré, Vol. 23, 1987, pp. 135-178. Zbl0633.60110MR891708
  3. [3] P. Dai Pra, Space-time large deviations for interacting particle systems, Comm. Pure Appl. Math., Vol. XLVI, 1993, pp. 387-422. Zbl0797.60028MR1202962
  4. [4] P. Dai Pra, Large deviations and stationary measures for interacting particle systems, Stoch. Proc. Appl., Vol. 48, 1993, pp. 9-30. Zbl0789.60020MR1237166
  5. [5] P. Diaconis and L. Saloff-Coste, Logarithmic Sobolev inequalities and finite Markov chains, preprint. 
  6. [6] P.A. Ferrari, A. Galves and C. Landim, Exponential waiting time for a big gap in a one-dimensional zero-range process, Ann. Prob., Vol. 22, n. 1, 1994, pp. 284-288. Zbl0793.60108MR1258878
  7. [7] P.A. Ferrari, A. Galves and T.M. Liggetf, Exponential waiting time for filling a large interval in the symmetric simple exclusion process, Ann. Inst. Poincare, Prob. Stat., Vol. 31, n. 1, 1995, pp. 155-175. Zbl0819.60095MR1340035
  8. [8] M.I. Freidlin and A.D. Wentzell, Random perturbations of dynamical systems, Springer-Verlag, 1984. Zbl0522.60055MR722136
  9. [9] T.E. Harris, First passage and recurrence distribution, Trans. Am. Math. Soc., Vol. 73, 1952, pp. 471-486. Zbl0048.36301MR52057
  10. [10] R. Holley and D. Stroock, Applications of the stochastic Ising model to the Gibbs states, Comm. Math. Phys., Vol. 48, 1976, pp. 249-265. MR428984
  11. [11] H. Kunsch, Non reversible stationary measures for infinite IPS, Z. Wahrsch. Verw. Gebiete, Vol. 66, 1984, pp. 407-424. Zbl0541.60098MR751579
  12. [12] J.L. Lebowitz and R.H. Schonmann, On the asymtotics of occurrence times of rare events for stochastic spin systems, J. Stat. Phys., Vol. 48, n. 3/4, 1987, pp. 727-751. Zbl1084.82521MR914904
  13. [13] T.M. Liggett, Interacting Particle Systems, Springer, 1985. Zbl0559.60078MR776231
  14. [ 14] F. Martinelli, E. Olivieri and E. Schonmann, Comm. Math. Phys., Vol. 165, 33, 1994. Zbl0811.60097MR1298940
  15. [15] F. Martinelli, E. Olivieri and E. Scoppola, Metastability and exponential approach to equilibrium for low temperature stochastic Ising models, J. Stat. Phys., Vol. 61, 1990, pp. 1105. Zbl0739.60096MR1083898
  16. [16] E.J. Neves and R.H. Schonmann, Critical droplets and metastability for a Glauber dynamics at very low temperatures, Comm. Math. Phys., Vol. 137, 1991, pp. 209-230. Zbl0722.60107MR1101685
  17. [17] E.J. Neves and R.H. Schonmann, Behavior of droplets for a class of Glauber dynamics at very low temperatures, Prob. Th. Rel. Fields, Vol. 91, 1992, pp. 331. Zbl0739.60101MR1151800
  18. [18] S. Olla, Large deviations for Gibbs random fields, Prob. Th. Rel. Fields, Vol. 77, 1988, pp. 343-357. Zbl0621.60031MR931502
  19. [19] E. Olivieri and E. Scoppola, Markov chains with exponentially small transition probabilities: first exit problem from a general domain. I. The reversible case, J. Stat. Phys., Vol. 79, 1995, pp. 613-647. Zbl1081.60541MR1327899
  20. [20] E. Olivieri and E. Scoppola, Markov chains with exponentially small transition probabilities: first exit problem from a general domain. II. The general case, to appear in J. Stat. Phys. Zbl1081.60542MR1412076
  21. [21] S.L. Lu and H.-T. Yau, Spectral gap and logarithmic Sobolev inequalities for Kawasaki and Glauber dynamics, C.M.P., Vol. 156, 1993, pp. 399-433. Zbl0779.60078MR1233852

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