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Asymptotic Entropy of Random Walks on Regular Languages over a Finite Alphabet
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.Comment: 47 pages, 2 figure