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2008 | 6 | 2 | 237-261
Tytuł artykułu

Characterization of equilibrium measures for critical reversible Nearest Particle Systems

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We show that for critical reversible attractive Nearest Particle Systems all equilibrium measures are convex combinations of the upper invariant equilibrium measure and the point mass at all zeros, provided the underlying renewal sequence possesses moments of order strictly greater than $$ \frac{{7 + \sqrt {41} }} {2} $$ and obeys some natural regularity conditions.
Słowa kluczowe
Wydawca
Czasopismo
Rocznik
Tom
6
Numer
2
Strony
237-261
Opis fizyczny
Daty
wydano
2008-06-01
online
2008-04-15
Twórcy
autor
Bibliografia
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  • [4] Griffeath D., Liggett T.M., Critical phenomena for Spitzer’s reversible nearest particle systems, Ann. Probab., 1982, 10, 881–895 http://dx.doi.org/10.1214/aop/1176993711
  • [5] Liggett T.M., Interacting particle systems, Springer-Verlag, New York, 1985
  • [6] Liggett T.M., L 2 rates of convergence for attractive reversible nearest particle systems: the critical case, Ann. Probab., 1991, 19, 935–959 http://dx.doi.org/10.1214/aop/1176990330
  • [7] Liggett T.M., Branching random walks and contact processes on homogenous trees, Probab. Theory Related Fields, 1996, 106, 495–519 http://dx.doi.org/10.1007/s004400050073
  • [8] Mountford T., A complete convergence theorem for attractive reversible nearest particle systems, Canad. J. Math., 1997, 49, 321–337
  • [9] Mountford T., A convergence result for critical reversible nearest particle systems, Ann. Probab., 2002, 30, 1–61
  • [10] Mountford T., Sweet T., Finite approximations to the critical reversible nearest particle system, Ann. Probab., 1998, 26, 1751–1780 http://dx.doi.org/10.1214/aop/1022855881
  • [11] Mountford T., Wu L.C., The time for a critical nearest particle system to reach equilibrium starting with a large gap, Electron. J. Probab., 2005, 10, 436–498
  • [12] Schinazi R., Brownian fluctuations of the edge for critical reversible nearest-particle systems, Ann. Probab., 1992, 20, 194–205 http://dx.doi.org/10.1214/aop/1176989924
  • [13] Sinclair A., Jerrum M., Approximate counting uniform generation and rapidly mixing Markov chains, Inform. and Comput., 1989, 82, 93–133 http://dx.doi.org/10.1016/0890-5401(89)90067-9
  • [14] Spitzer F., Stochastic time evolution of one dimensional infinite particle systems, Bull. Amer. Math. Soc., 1977, 83, 880–890 http://dx.doi.org/10.1090/S0002-9904-1977-14322-X
  • [15] Sweet T.D., One dimensional spin systems, PhD thesis, University of California, Los Angeles, USA, 1997
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-008-0024-x
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