Heat kernel asymptotics for scaling limits of isoradial graphs

2023/01/17 by Simon Schwarz, Schwarz, Simon, Anja Sturm +3
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR) #Spectral Theory in Mathematical Physics #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2301.06852

openalex publication_date 2023/01/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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