Let be a locally compact non-compact metric group. Assuming that is abelian we construct symmetric aperiodic random walks on with probabilities 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 can be made as slow as possible by choosing appropriate aperiodic random walks Sₙ on .
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm118-2-6,
author = {Alexander Bendikov and Barbara Bobikau},
title = {Long time behavior of random walks on abelian groups},
journal = {Colloquium Mathematicae},
volume = {120},
year = {2010},
pages = {445-464},
zbl = {1196.60079},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm118-2-6}
}
Alexander Bendikov; Barbara Bobikau. Long time behavior of random walks on abelian groups. Colloquium Mathematicae, Tome 120 (2010) pp. 445-464. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm118-2-6/