Random walks on finite rank solvable groups

Pittet, 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 -