Heat kernel estimates on book-like graphs

Fuente: arXiv
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Autores principales: Dautenhahn, Emily, Saloff-Coste, Laurent
Formato: Preprint
Publicado: 2026
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author Dautenhahn, Emily
Saloff-Coste, Laurent
author_facet Dautenhahn, Emily
Saloff-Coste, Laurent
contents In this paper, we prove two-sided heat kernel estimates on what we call "book-like" graphs. These are graphs consisting of pieces that satisfy the parabolic Harnack inequality that are glued together in a sufficiently nice way over a possibly infinite set of vertices. The prototypical example is gluing a copy of the square four-dimensional lattice $\mathbb{Z}^4,$ a copy of $\mathbb{Z}^5$, and a copy of $\mathbb{Z}^6$ by identifying their $x_1$-axes and taking the lazy simple random walk on this glued graph. Our results are flexible enough to handle perturbations of this example, for instance by adding diagonals to one of the lattices or a few extra vertices/edges.
format Preprint
id arxiv_https___arxiv_org_abs_2603_04617
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Heat kernel estimates on book-like graphs
Dautenhahn, Emily
Saloff-Coste, Laurent
Probability
60J10 (Primary), 60G50, 35K08 (Secondary)
In this paper, we prove two-sided heat kernel estimates on what we call "book-like" graphs. These are graphs consisting of pieces that satisfy the parabolic Harnack inequality that are glued together in a sufficiently nice way over a possibly infinite set of vertices. The prototypical example is gluing a copy of the square four-dimensional lattice $\mathbb{Z}^4,$ a copy of $\mathbb{Z}^5$, and a copy of $\mathbb{Z}^6$ by identifying their $x_1$-axes and taking the lazy simple random walk on this glued graph. Our results are flexible enough to handle perturbations of this example, for instance by adding diagonals to one of the lattices or a few extra vertices/edges.
title Heat kernel estimates on book-like graphs
topic Probability
60J10 (Primary), 60G50, 35K08 (Secondary)
url https://arxiv.org/abs/2603.04617