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Heat Kernel Asymptotics on the Lamplighter Group

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Heat Kernel Asymptotics on the Lamplighter Group
2.	Creator	Author's name, affiliation, country	David Revelle; UC Berkeley
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)
4.	Description	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 $\alpha$.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	2003-11-10
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ecp.ejpecp.org/article/view/1092
10.	Identifier	Digital Object Identifier	10.1214/ECP.v8-1092
11.	Source	Journal/conference title; vol., no. (year)	Electronic Communications in Probability; Vol 8
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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