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

2013/04/12 by Gilch, Lorenz A.
#FOS: Mathematics #Primary: 60J10 #Probability (math.PR) #Secondary: 28D20

paper · doi:10.48550/arxiv.1304.3555

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.

Related

• Analyticity of the entropy for some random walks
• Average Entropy of the Ranges for Simple Random Walks on Discrete Groups
• Sharp lower bounds for the asymptotic entropy of symmetric random walks
• Drift and entropy growth for random walks on groups
• Branching Frequency and Markov Entropy of Repetition-Free Languages