An inequality for the heat kernel on an Abelian Cayley graph

2016/12/21 by Price, Thomas McMurray
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1612.07306

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 ≤ t', (H_t(u, v))/(H_t(u,u)) ≤ \fracH_t'(u, v)H_t'(u,u) This was an open problem posed by Regev and Shinkar.

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