# Random walks on finite rank solvable groups

Ch. Pittet; Laurent Saloff-Coste

Journal of the European Mathematical Society (2003)

- Volume: 005, Issue: 4, page 313-342
- ISSN: 1435-9855

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topPittet, Ch., and Saloff-Coste, Laurent. "Random walks on finite rank solvable groups." Journal of the European Mathematical Society 005.4 (2003): 313-342. <http://eudml.org/doc/277607>.

@article{Pittet2003,

abstract = {We establish the lower bound $p_\{2t\}(e,e)\succsim \operatorname\{exp\}(−t^\{1/3\})$, for the large times asymptotic behaviours of the probabilities $p_\{2t\}(e,e)$ 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 $r$.)},

author = {Pittet, Ch., Saloff-Coste, Laurent},

journal = {Journal of the European Mathematical Society},

keywords = {random walk; heat kernel decay; asymptotic invariants of infinite groups; Prüfer rank; solvable group; random walks; heat kernel decay; asymptotic invariants of infinite groups; Prüfer rank; solvable groups; finite symmetric generating sets; finitely generated groups; word metrics},

language = {eng},

number = {4},

pages = {313-342},

publisher = {European Mathematical Society Publishing House},

title = {Random walks on finite rank solvable groups},

url = {http://eudml.org/doc/277607},

volume = {005},

year = {2003},

}

TY - JOUR

AU - Pittet, Ch.

AU - Saloff-Coste, Laurent

TI - Random walks on finite rank solvable groups

JO - Journal of the European Mathematical Society

PY - 2003

PB - European Mathematical Society Publishing House

VL - 005

IS - 4

SP - 313

EP - 342

AB - We establish the lower bound $p_{2t}(e,e)\succsim \operatorname{exp}(−t^{1/3})$, for the large times asymptotic behaviours of the probabilities $p_{2t}(e,e)$ 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 $r$.)

LA - eng

KW - random walk; heat kernel decay; asymptotic invariants of infinite groups; Prüfer rank; solvable group; random walks; heat kernel decay; asymptotic invariants of infinite groups; Prüfer rank; solvable groups; finite symmetric generating sets; finitely generated groups; word metrics

UR - http://eudml.org/doc/277607

ER -

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