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Non-abelian free group actions: Markov processes, the Abramov–Rohlin formula and Yuzvinskii’s formula

Published online by Cambridge University Press:  13 October 2009

LEWIS BOWEN
LEWIS BOWEN*
Affiliation:
Mailstop 3368, Texas A&M University, College Station, TX 77843-3368, USA (email: lpbowen@math.tamu.edu)
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Abstract

This paper introduces Markov chains and processes over non-abelian free groups and semigroups. We prove a formula for the f-invariant of a Markov chain over a free group in terms of transition matrices that parallels the classical formula for the entropy a Markov chain. Applications include free group analogues of the Abramov–Rohlin formula for skew-product actions and Yuzvinskii’s addition formula for algebraic actions.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 30 , Issue 6 , December 2010 , pp. 1629 - 1663
Copyright
Copyright © Cambridge University Press 2009

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