The parametrix construction of the heat kernel on a graph

2023/08/08 by Gautam Chinta, Jay Jorgenson, Chinta, Gautam +5 · 1 citation
Computer Science · Engineering · Mathematics · #05C50 #33C10 #39A12 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Analysis Techniques #Analysis of PDEs (math.AP) #Combinatorics (math.CO) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Primary: 35K08 #Secondary:35K05

paper · pdf · doi:10.48550/arxiv.2308.04174

openalex publication_date 2023/08/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we develop the parametrix approach for constructing the heat kernel on a graph G. In particular, we highlight two specific cases. First, we consider the case when G is embedded in a Eulidean domain or manifold Ω, and we use a heat kernel associated to Ω to obtain a formula for the heat kernel on G. Second, we consider when G is a subgraph of a larger graph \widetildeG, and we obtain a formula for the heat kernel on G from the heat kernel on \widetildeG restricted to G.

Cited by

• Semi-discrete heat equations with variable coefficients and the parametrix method

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