On the Critical Dimension and AC Entropy for Markov Odometers

• Autores: Anthony H. Dooley, Genevieve Mortiss
• Localización: Monatshefte für mathematik, ISSN 0026-9255, Vol. 149, Nº 3, 2006, págs. 193-213
• Idioma: inglés
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• Resumen

  • 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.