Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Ergodic theorems for the asymmetric simple exclusion process


Author: Thomas M. Liggett
Journal: Trans. Amer. Math. Soc. 213 (1975), 237-261
MSC: Primary 60K35
MathSciNet review: 0410986
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Consider the infinite particle system on the integers with the simple exclusion interaction and one-particle motion determined by $ p(x,x + 1) = p$ and $ p(x,x - 1) = q$ for $ x \in Z$, where $ p + q = 1$ and $ p > q$. If $ \mu $ is the initial distribution of the system, let $ {\mu _t}$ be the distribution at time t. The main results determine the limiting behavior of $ {\mu _t}$ as $ t \to \infty $ for simple choices of $ \mu $. For example, it is shown that if $ \mu $ is the pointmass on the configuration in which all sites to the left of the origin are occupied, while those to the right are vacant, then the system converges as $ t \to \infty $ to the product measure on $ {\{ 0,1\} ^Z}$ with density $ {\raise0.5ex\hbox{$\scriptstyle 1$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 2$}}$. For the proof, an auxiliary process is introduced which is of interest in its own right. It is a process on the positive integers in which particles move according to the simple exclusion process, but with the additional feature that there can be creation and destruction of particles at one. Ergodic theorems are proved for this process also.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 60K35

Retrieve articles in all journals with MSC: 60K35


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1975-0410986-7
PII: S 0002-9947(1975)0410986-7
Keywords: Infinite particle systems, simple exclusion process
Article copyright: © Copyright 1975 American Mathematical Society