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Random Walks on Groups and Monoids with a Markovian Harmonic Measure


 
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1. Title Title of document Random Walks on Groups and Monoids with a Markovian Harmonic Measure
 
2. Creator Author's name, affiliation, country Mairesse Jean; CNRS - Universite Paris 7
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Finitely generated group or monoid; free product; random walk; harmonic measure.
 
3. Subject Subject classification Primary 60J10, 60B15, 31C05; Secondary 60J22, 65C40, 20F65.
 
4. Description Abstract 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.
 
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7. Date (YYYY-MM-DD) 2005-12-16
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/293
 
10. Identifier Digital Object Identifier 10.1214/EJP.v10-293
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 10
 
12. Language English=en
 
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