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On extremal measures for conservative particle systems. (English) Zbl 0981.60098

Author’s abstract: It is well known that the exclusion, zero-range and misanthrope particle systems possess families of invariant measures due to the mass conservation property. Although these families have been classified a great deal, a full characterization of their extreme points is not available. We consider an approach to the study of this classification. One of the results is that the zero-range product invariant measures, \(\prod_{i\in S}\mu_{\alpha(\cdot)}\), for an infinite countable set \(S\), under mild conditions, are identified as extremal for \(\alpha(\cdot)\in H_{ZR}\), where \(\mu_{\alpha(i)}(k)= Z(\alpha(i))^{-1} \alpha(i)^k/g(1)\cdots g(k)\) with \(g\) and \(Z\) the rate function and normaliation, respectively, and \(H_{ZR}\) is the set of invariant measures for the transition probability \(p\).

MSC:

60K35 Interacting random processes; statistical mechanics type models; percolation theory
60F05 Central limit and other weak theorems
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