Every recurrent network has a potential tending to infinity
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866913705147498496 |
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| author | Nachmias, Asaf Peres, Yuval |
| author_facet | Nachmias, Asaf Peres, Yuval |
| contents | A rooted network consists of a connected, locally finite graph G, equipped with edge conductances and a distinguished vertex o. A nonnegative function on the vertices of G which vanishes at o, has Laplacian 1 at o, and is harmonic at all other vertices is called a potential. We prove that every infinite recurrent rooted network admits a potential tending to infinity. This is an analogue of classical theorems due to Evans and Nakai in the settings of Euclidean domains and Riemannian surfaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_17285 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Every recurrent network has a potential tending to infinity Nachmias, Asaf Peres, Yuval Probability Analysis of PDEs A rooted network consists of a connected, locally finite graph G, equipped with edge conductances and a distinguished vertex o. A nonnegative function on the vertices of G which vanishes at o, has Laplacian 1 at o, and is harmonic at all other vertices is called a potential. We prove that every infinite recurrent rooted network admits a potential tending to infinity. This is an analogue of classical theorems due to Evans and Nakai in the settings of Euclidean domains and Riemannian surfaces. |
| title | Every recurrent network has a potential tending to infinity |
| topic | Probability Analysis of PDEs |
| url | https://arxiv.org/abs/2502.17285 |