Lorenz A. Gilch

Rate of Escape of Random Walks on Regular Languages and Free Products by Amalgamation of Finite Groups
dmtcs:3580 
Discrete Mathematics & Theoretical Computer Science,
January 1, 2008,
DMTCS Proceedings vol. AI, Fifth Colloquium on Mathematics and Computer Science

https://doi.org/10.46298/dmtcs.3580
Rate of Escape of Random Walks on Regular Languages and Free Products by Amalgamation of Finite Groups
Authors: Lorenz A. Gilch ^{1}
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Lorenz A. Gilch
1 Institut für Mathematische Strukturtheorie (Math C)
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.
ConchonKerjan, Guillaume, 2022, Cutoff For Random Lifts Of Weighted Graphs, The Annals Of Probability, 50, 1, 10.1214/21aop1534.
Gilch, Lorenz A., 2016, Asymptotic Entropy Of Random Walks On Regular Languages Over A Finite Alphabet, Electronic Journal Of Probability, 21, none, 10.1214/16ejp4180.
Ledrappier, Franรงois, 2013, Regularity Of The Entropy For Random Walks On Hyperbolic Groups, The Annals Of Probability, 41, 5, 10.1214/12aop748.