Heat Kernel Asymptotics for Scaling Limits of Isoradial Graphs

Abstract We consider the asymptotics of the discrete heat kernel on isoradial graphs for the case where the time and the edge lengths tend to zero simultaneously. Depending on the asymptotic ratio between time and edge lengths, we show that two different regimes arise: (i) a Gaussian regime and (ii)...

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Bibliographic Details
Published inPotential analysis
Main Authors Schwarz, Simon, Sturm, Anja, Wardetzky, Max
Format Journal Article
LanguageEnglish
Published 31.07.2024
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Summary:Abstract We consider the asymptotics of the discrete heat kernel on isoradial graphs for the case where the time and the edge lengths tend to zero simultaneously. Depending on the asymptotic ratio between time and edge lengths, we show that two different regimes arise: (i) a Gaussian regime and (ii) a Poissonian regime, which resemble the short-time asymptotics of the heat kernel on (i) Euclidean spaces and (ii) graphs, respectively.
ISSN:0926-2601
1572-929X
DOI:10.1007/s11118-024-10161-5