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arXiv:1612.07306math.PR

An inequality for the heat kernel on an Abelian Cayley graph

Thomas McMurray Price

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Abstract

We demonstrate a relationship between the heat kernel on a finite weighted Abelian Cayley graph and Gaussian functions on lattices. This can be used to prove a new inequality for the heat kernel on such a graph: when $t \leq t'$, $$\frac{H_t(u, v)}{H_t(u,u)} \leq \frac{H_{t'}(u, v)}{H_{t'}(u,u)}$$ This was an open problem posed by Regev and Shinkar.

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math.PRProbability

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