| Título: | Random Walks on Groups and Monoids with a Markovian Harmonic Measure |
| Autores: | Jean, Mairesse; CNRS - Universite Paris 7 |
| Fecha: | 2005-01-01 |
| Publicador: | Electronic journal of probability |
| Fuente: |
 |
| Tipo: |
Peer-reviewed Article |
| Tema: |
Finitely generated group or monoid; free product; random walk; harmonic measure. Primary 60J10, 60B15, 31C05; Secondary 60J22, 65C40, 20F65. |
| Descripción: | We consider a transient nearest neighbor random walk on a group $G$ with finite set of generators $S$. The pair $(G,S)$ is assumed to admit a natural notion of normal form words where only the last letter is modified by multiplication by a generator. The basic examples are the free products of a finitely generated free group and a finite family of finite groups, with natural generators. We prove that the harmonic measure is Markovian of a particular type. The transition matrix is entirely determined by the initial distribution which is itself the unique solution of a finite set of polynomial equations of degree two. This enables to efficiently compute the drift, the entropy, the probability of ever hitting an element, and the minimal positive harmonic functions of the walk. The results extend to monoids. |
| Idioma: | No aplica |
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