Affordable Access

Access to the full text

The problem of describing central measures on the path spaces of graded graphs

Authors
  • Vershik, A. M.1
  • 1 St. Petersburg State University Institute for Information Transmission Problems, St. Petersburg Department of Steklov Institute of Mathematics, St.-Petersburg, Russia , St.-Petersburg (Russia)
Type
Published Article
Journal
Functional Analysis and Its Applications
Publisher
Springer US
Publication Date
Dec 17, 2014
Volume
48
Issue
4
Pages
256–271
Identifiers
DOI: 10.1007/s10688-014-0069-5
Source
Springer Nature
Keywords
License
Yellow

Abstract

We suggest a new method for describing invariant measures on Markov compacta and on path spaces of graphs and, thereby, for describing characters of certain groups and traces of AF-algebras. The method relies on properties of filtrations associated with a graph and, in particular, on the notion of a standard filtration. The main tool is an intrinsic metric introduced on simplices of measures; this is an iterated Kantorovich metric, and the central result is that the relative compactness in this metric guarantees the possibility of a constructive enumeration of ergodic invariant measures. Applications include a number of classical theorems on invariant measures.

Report this publication

Statistics

Seen <100 times