A characterization of the invariant measures for an infinite particle system with interactions
A characterization of the invariant measures for an infinite particle system with interactions
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DOI：
10.1090/s0002-9947-1973-0326867-1
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发表时间：
1973-05
影响因子：
1.3
通讯作者：
T. Liggett
中科院分区：
文献类型：
--
作者：
T. Liggett
摘要。设p（x,y）为可数集合S上对称的、不可约的瞬态马尔可夫链的过渡函数，设71为S上具有简单排斥相互作用和由p决定的单粒子运动的无限粒子系统。用S上关于p（x,y）调和的有界函数，得到了71的所有不变测度的表征。证明了关于系统收敛于不变测度的遍历定理。
ABSTRACT. Let p(x,y) be the transition function for a symmetric, irreducible, transient Markov chain on the countable set S. Let 71 be the infinite particle system on S with the simple exclusion interaction and one-particle motion determined by p. A characterization is obtained of all the invariant measures for 71 in terms of the bounded functions on S which are harmonic with respect to p(x,y). Ergodic theorems are proved concerning the convergence of the system to an invariant measure.