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

Lorenz Alexander Gilch

doi:10.1214/16-EJP4180

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

Lorenz Alexander Gilch

Institute of Discrete Mathematics (5050)

Research output: Contribution to journal › Article › peer-review

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 language	English
Pages (from-to)	1-42
Journal	Electronic Journal of Probability
Volume	21
Issue number	8
DOIs	https://doi.org/10.1214/16-EJP4180
Publication status	Published - 2016

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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.",

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AB - 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.

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JO - Electronic Journal of Probability

JF - Electronic Journal of Probability

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

Abstract

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