Asymptotic Entropy of Random Walks on Regular Languages over a Finite Alphabet

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Abstract

We prove existence of asymptotic entropy of random walks on regular languages over a finite alphabet and we give formulas for it. Furthermore, we show that the entropy varies real-analytically in terms of probability measures of constant support, which describe the random walk. This setting applies, in particular, to random walks on virtually free groups.
Original languageEnglish
Pages (from-to)1-42
JournalElectronic Journal of Probability
Volume21
Issue number8
DOIs
Publication statusPublished - 2016

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