Geodesic
Rate of Escape of Random Walks on Regular Languages and Free Products by Amalgamation of Finite Groups
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AI, Fifth Colloquium on Mathematics and Computer Science, DMTCS Proceedings vol. AI, Fifth Colloquium on Mathematics and Computer Science (2008).

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We consider random walks on the set of all words over a finite alphabet such that in each step only the last two letters of the current word may be modified and only one letter may be adjoined or deleted. We assume that the transition probabilities depend only on the last two letters of the current word. Furthermore, we consider also the special case of random walks on free products by amalgamation of finite groups which arise in a natural way from random walks on the single factors. The aim of this paper is to compute several equivalent formulas for the rate of escape with respect to natural length functions for these random walks using different techniques. 
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     author = {Gilch, Lorenz A.},
     title = {Rate of {Escape} of {Random} {Walks} on {Regular} {Languages} and {Free} {Products} by {Amalgamation} of {Finite} {Groups}},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AI, Fifth Colloquium on Mathematics and Computer Science},
     year = {2008},
     doi = {10.46298/dmtcs.3580},
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     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3580/}
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Gilch, Lorenz A. Rate of Escape of Random Walks on Regular Languages and Free Products by Amalgamation of Finite Groups. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AI, Fifth Colloquium on Mathematics and Computer Science, DMTCS Proceedings vol. AI, Fifth Colloquium on Mathematics and Computer Science (2008). doi : 10.46298/dmtcs.3580. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3580/

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