The problem of describing central measures on path space of graded graphs
Representation Theory
2014-08-15 v1
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
Keywords
Cite
@article{arxiv.1408.3291,
title = {The problem of describing central measures on path space of graded graphs},
author = {Anatoly Vershik},
journal= {arXiv preprint arXiv:1408.3291},
year = {2014}
}
Comments
28pp. Ref 18