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- W2003751012 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 $alpha$." @default.
- W2003751012 created "2016-06-24" @default.
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- W2003751012 date "2003-01-01" @default.
- W2003751012 modified "2023-09-23" @default.
- W2003751012 title "Heat Kernel Asymptotics on the Lamplighter Group" @default.
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- W2003751012 doi "https://doi.org/10.1214/ecp.v8-1092" @default.
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