Heat kernel estimates on book-like graphs
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866910041593872384 |
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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 |