2014/08/14 by A. M. Vershik, Anatoly Vershik, Vershik, Anatoly
Computer Science · Mathematics · #Graph theory and applications #Matrix Theory and Algorithms #Topological and Geometric Data Analysis #math.RT #msc:05C63 #msc:05E10 #msc:20C32 #msc:60J05
paper · pdf · doi:10.48550/arxiv.1408.3291
28pp. Ref 18
arxiv created 2014/08/14 · arxiv updated 2014/08/15
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