Processus des misanthropes

  • Christiane Cocozza-Thivent
Article

Summary

We consider a system of identical interacting particles moving on the lattice ℤ d . The rate at which a particle at the site x jumps to the site y is p(y−x)b(η(x), η(y)) where p is an irreducible probability on ℤ d and b(η(x), η(y)) is an increasing (resp. decreasing) function of the number η(x) (resp. η(y)) of particles at site x (resp. y). We study the convergence of the system to equilibrium and describe the invariant measures.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliographie

  1. 1.
    Andjel, E.: Invariant measures for the zero range process. Ann. Prob. 10, 525–547 (1982)Google Scholar
  2. 2.
    Andjel, E.: The asymetric simple exclusion process on ℤd. Z. Wahrscheinlichkeitstheor. Verw. Geb. 58, 423–432 (1981)Google Scholar
  3. 3.
    Cocozza, Ch., Kipnis, C.: Processus de vie et mort sur ℝ avec interaction selon les particules les plus proches. Z. Wahrscheinlichkeitstheor. Verw. Geb. 51, 123–132 (1980)Google Scholar
  4. 4.
    Cocozza, Ch., Roussignol, M.: Unicité d'un processus de naissance et mort sur la droite réelle. Annales de l'IHP 15, 93–105 (1979)Google Scholar
  5. 5.
    Holley, R., Stroock, D.: A martingale approach to infinite systems of interacting processes. Ann. Probab. 4, 195–228 (1976)Google Scholar
  6. 6.
    Holley, R., Stroock, D.: Nearest neighbor birth and death processes on the real line. Acta Math. 140, 103–154 (1978)Google Scholar
  7. 7.
    Liggett, T.: The stochastic evolution of infinite systems for interacting particles. Lecture Notes in Math. n∘ 598; Ecole d'Eté de probabilités de Saint-Flour VI, 1976. Berlin-Heidelberg-New York: Springer 1977Google Scholar
  8. 8.
    Liggett, T.: Interacting particle systems. [à paraître chez Springer]Google Scholar
  9. 9.
    Spitzer, F.: Interacting Markov processes. Adv. Math. 5, 246–290 (1970)Google Scholar

Copyright information

© Springer-Verlag 1985

Authors and Affiliations

  • Christiane Cocozza-Thivent
    • 1
  1. 1.Laboratoire de Probabilités - Tour 56Université Paris VIParis Cedex 05France

Personalised recommendations