@article{ECP1092,
author = {David Revelle},
title = {Heat Kernel Asymptotics on the Lamplighter Group},
journal = {Electron. Commun. Probab.},
fjournal = {Electronic Communications in Probability},
volume = {8},
year = {2003},
keywords = {},
abstract = {We show that, for one generating set, the on-diagonal decay of the heat kernel on the lamplighter group is asymptotic to $c_1 n^{1/6}\exp[-c_2 n^{1/3}]$. We also make off-diagonal estimates which show that there is a sharp threshold for which elements have transition probabilities that are comparable to the return probability. The off-diagonal estimates also give an upper bound for the heat kernel that is uniformly summable in time. The methods used also apply to a one dimensional trapping problem, and we compute the distribution of the walk conditioned on survival as well as a corrected asymptotic for the survival probability. Conditioned on survival, the position of the walker is shown to be concentrated within $\alpha n^{1/3}$ of the origin for a suitable $\alpha$.},
pages = {no. 16, 142-154},
issn = {1083-589X},
doi = {10.1214/ECP.v8-1092},
url = {http://ecp.ejpecp.org/article/view/1092}}