Summary
It has been conjectured that the asymmetric exclusion process starting from certain product measures converges to a non extremal equilibrium measure. In this paper we prove a weaker version of this conjecture.
References
Andjel, E.: The asymmetric simple exclusion process on ℤd. Z. Wahrscheinlichkeitstheor. Verw. Geb.58, 423–432 (1981)
Liggett, T.: Ergodic theorems for the asymmetric simple exclusion process. Trans. Am. Math. Soc.213, 237–261 (1975)
Liggett, T.: Coupling the simple exclusion process. Ann. Probab.4, 339–356 (1976)
Liggett, T.: Ergodic theorems for the asymmetric simple exclusion process II. Ann. Probab.5, 795–801 (1977)
Liggett, T.: Interacting Particle systems. Berlin Heidelberg New York: Springer 1985
Phelps, R.: Lectures on Choquet's theorem. Princeton: Van Nostrand 1965
Rost, H.: Non equilibrium behaviour of a many Particle process: Density profile and local equilibria. Z. Wahrscheinlichkeitstheor. Verw. Geb.58, 41–53 (1981)
Spitzer, F.: Interaction of Markov processes. Adv. Math.5, 246–290 (1970)
Walters, P.: An introduction to ergodic theory. Berlin Heidelberg New York: Springer 1982
Wick, D.: A Dynamical phase transition in an infinite particle system. J. Stat. Phys.38, 516 (1985)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Andjel, E.D. Convergence to a non extremal equilibrium measure in the exclusion process. Probab. Th. Rel. Fields 73, 127–134 (1986). https://doi.org/10.1007/BF01845996
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01845996
Keywords
- Stochastic Process
- Probability Theory
- Mathematical Biology
- Product Measure
- Weak Version