TY - JOUR
T1 - On the critical dimension and AC entropy for Markov odometers
AU - Dooley, A. H.
AU - Mortiss, G.
PY - 2006/11/1
Y1 - 2006/11/1
N2 - 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.
AB - 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.
UR - http://dx.doi.org/10.1007/s00605-005-0372-6
UR - https://www.scopus.com/pages/publications/33750081738
U2 - 10.1007/s00605-005-0372-6
DO - 10.1007/s00605-005-0372-6
M3 - Article
SN - 0026-9255
VL - 149
SP - 193
EP - 213
JO - Monatshefte fur Mathematik
JF - Monatshefte fur Mathematik
IS - 3
ER -