Heat Kernel Asymptotics for Scaling Limits of Isoradial Graphs

IF 1 3区数学 Q1 MATHEMATICS

Potential Analysis Pub Date : 2024-07-31 DOI:10.1007/s11118-024-10161-5

Simon Schwarz, Anja Sturm, Max Wardetzky

引用次数: 0

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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等轴图缩放极限的热核渐近法

我们考虑了时间和边长同时趋于零的情况下等边图上离散热核的渐近线。根据时间和边长之间的渐近比，我们证明会出现两种不同的状态：(i) 高斯状态和 (ii) 泊松状态，它们分别类似于热核在 (i) 欧几里得空间和 (ii) 图上的短时渐近。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Potential Analysis 数学-数学

CiteScore

2.20

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： The journal publishes original papers dealing with potential theory and its applications, probability theory, geometry and functional analysis and in particular estimations of the solutions of elliptic and parabolic equations; analysis of semi-groups, resolvent kernels, harmonic spaces and Dirichlet forms; Markov processes, Markov kernels, stochastic differential equations, diffusion processes and Levy processes; analysis of diffusions, heat kernels and resolvent kernels on fractals; infinite dimensional analysis, Gaussian analysis, analysis of infinite particle systems, of interacting particle systems, of Gibbs measures, of path and loop spaces; connections with global geometry, linear and non-linear analysis on Riemannian manifolds, Lie groups, graphs, and other geometric structures; non-linear or semilinear generalizations of elliptic or parabolic equations and operators; harmonic analysis, ergodic theory, dynamical systems; boundary value problems, Martin boundaries, Poisson boundaries, etc.