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arXiv · 1408.3291

The problem of describing central measures on path space of graded graphs

Anatoly Vershik
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Abstract

We suggest a new method of describing invariant measures on Markov compacta and path spaces of graphs, and thus of describing characters of some groups and traces of AF-algebras. The method relies on properties of filtrations associated with the graph and, in particular, on the notion of a standard filtration. The main tool is the so-called internal metric that we introduce on simplices of measures; it is an iterated Kantorovich metric, and the key result is that the relative compactness in this metric guarantees a constructive enumeration of the ergodic invariant measures. Applications include a number of classical theorems on invariant measures

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Anatoly Vershik. 2014-08-14. The problem of describing central measures on path space of graded graphs. https://arxiv.org/abs/1408.3291

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