Geodesic
Random walks on finite rank solvable groups
Journal of the European Mathematical Society, Tome 5 (2003) no. 4, pp. 313-342 Cet article a éte moissonné depuis la source EMS Press

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We establish the lower bound p2t(e,e)scapexp(-t1/3), for the large times asymptotic behaviours of the probabilities p2t(e,e) of return to the origin at even times 2t, for random walks associated with finite symmetric generating sets of solvable groups of finite Prüfer rank. (A group has finite Prüfer rank if there is an integer r, such that any of its finitely generated subgroup admits a generating set of cardinality less or equal to r.)
DOI : 10.1007/s10097-003-0054-4
Classification : 20-XX, 60-XX, 82-XX, 00-XX
Keywords: random walk, heat kernel decay, asymptotic invariants of infinite groups, Prüfer rank, solvable group 
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     author = {Christophe Pittet and Laurent Saloff-Coste},
     title = {Random walks on finite rank solvable groups},
     journal = {Journal of the European Mathematical Society},
     pages = {313--342},
     year = {2003},
     volume = {5},
     number = {4},
     doi = {10.1007/s10097-003-0054-4},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s10097-003-0054-4/}
}
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Christophe Pittet; Laurent Saloff-Coste. Random walks on finite rank solvable groups. Journal of the European Mathematical Society, Tome 5 (2003) no. 4, pp. 313-342. doi: 10.1007/s10097-003-0054-4

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