Analysis of the physical Laplacian and the heat flow on a locally finite graph

TL;DR

This paper investigates the properties of the physical Laplacian and heat flow on infinite, locally finite graphs, including those with unbounded valence, to understand their mathematical and physical behaviors.

Contribution

It provides new insights into the analysis of the physical Laplacian and heat flow on infinite graphs with unbounded valence, expanding previous finite or bounded valence studies.

Findings

Characterization of the heat flow on infinite graphs

Analysis of the physical Laplacian's properties in unbounded valence cases

Extensions of classical results to more general graph structures

Abstract

We study the physical Laplacian and the corresponding heat flow on an infinite, locally finite graph with possibly unbounded valence.