Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.19256 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914255205302272 |
|---|---|
| author | Dautenhahn, Emily Saloff-Coste, Laurent |
| author_facet | Dautenhahn, Emily Saloff-Coste, Laurent |
| contents | Faber-Krahn functions provide lower bounds on the first Dirichlet eigenvalue of the Laplacian and are useful because they imply heat kernel upper bounds. In this paper, we are interested in Faber-Krahn functions and heat kernel estimates for a certain class of graphs consisting of "sufficiently nice pages" (satisfying a Harnack inequality) glued together via a "sufficiently nice spine." For such graphs, we obtain a relative Faber-Krahn function in terms of the Faber-Krahn functions on the pages. The corresponding heat kernel upper bound involves the volumes on the various pages. In the case our graphs satisfy a property we call "book-like" and the spine is appropriately transient, we provide a matching lower bound for the heat kernel between two points on the gluing spine. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_19256 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Faber-Krahn inequality and heat kernel estimates on glued graphs Dautenhahn, Emily Saloff-Coste, Laurent Probability 60J10 (Primary), 60G50, 35K08 Faber-Krahn functions provide lower bounds on the first Dirichlet eigenvalue of the Laplacian and are useful because they imply heat kernel upper bounds. In this paper, we are interested in Faber-Krahn functions and heat kernel estimates for a certain class of graphs consisting of "sufficiently nice pages" (satisfying a Harnack inequality) glued together via a "sufficiently nice spine." For such graphs, we obtain a relative Faber-Krahn function in terms of the Faber-Krahn functions on the pages. The corresponding heat kernel upper bound involves the volumes on the various pages. In the case our graphs satisfy a property we call "book-like" and the spine is appropriately transient, we provide a matching lower bound for the heat kernel between two points on the gluing spine. |
| title | Faber-Krahn inequality and heat kernel estimates on glued graphs |
| topic | Probability 60J10 (Primary), 60G50, 35K08 |
| url | https://arxiv.org/abs/2503.19256 |