On the critical dimension and AC entropy for Markov odometers

A. H. Dooley, G. Mortiss

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)

Abstract

Markov odometers are natural models for non-homogeneous Markov chains, and are natural generalisations of infinite product measures. We show how to calculate the critical dimension of these measures: this is an invariant which describes the asymptotic growth rate of sums of Radon-Nikodym derivatives. This interesting invariant appears to give a kind of entropy for non-singular odometer actions. The techniques require a law of large numbers for inhomogeneous Markov chains.
Original languageEnglish
Pages (from-to)193-213
JournalMonatshefte fur Mathematik
Volume149
Issue number3
DOIs
Publication statusPublished - 1 Nov 2006

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