Long time behavior of random walks on abelian groups

Alexander Bendikov, and Barbara Bobikau. "Long time behavior of random walks on abelian groups." Colloquium Mathematicae 118.2 (2010): 445-464. <http://eudml.org/doc/283430>.

@article{AlexanderBendikov2010,
abstract = {Let be a locally compact non-compact metric group. Assuming that is abelian we construct symmetric aperiodic random walks on with probabilities $n ↦ ℙ(S_\{2n\} ∈ V)$ of return to any neighborhood V of the neutral element decaying at infinity almost as fast as the exponential function n ↦ exp(-n). We also show that for some discrete groups , the decay of the function $n ↦ ℙ(S_\{2n\} ∈ V)$ can be made as slow as possible by choosing appropriate aperiodic random walks Sₙ on .},
author = {Alexander Bendikov, Barbara Bobikau},
journal = {Colloquium Mathematicae},
keywords = {locally compact abelian group; random walks},
language = {eng},
number = {2},
pages = {445-464},
title = {Long time behavior of random walks on abelian groups},
url = {http://eudml.org/doc/283430},
volume = {118},
year = {2010},
}

TY - JOUR
AU - Alexander Bendikov
AU - Barbara Bobikau
TI - Long time behavior of random walks on abelian groups
JO - Colloquium Mathematicae
PY - 2010
VL - 118
IS - 2
SP - 445
EP - 464
AB - Let be a locally compact non-compact metric group. Assuming that is abelian we construct symmetric aperiodic random walks on with probabilities $n ↦ ℙ(S_{2n} ∈ V)$ of return to any neighborhood V of the neutral element decaying at infinity almost as fast as the exponential function n ↦ exp(-n). We also show that for some discrete groups , the decay of the function $n ↦ ℙ(S_{2n} ∈ V)$ can be made as slow as possible by choosing appropriate aperiodic random walks Sₙ on .
LA - eng
KW - locally compact abelian group; random walks
UR - http://eudml.org/doc/283430
ER -