Stationary hitting times on vertex-transitive graphs
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866917188355489792 |
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| author | Berestycki, Nathanaël Hermon, Jonathan Teyssier, Lucas |
| author_facet | Berestycki, Nathanaël Hermon, Jonathan Teyssier, Lucas |
| contents | We prove a refined version of the Aldous and Brown's exponential approximation of stationary hitting times. These are valid for all reversible Markov chains. We then specialise our estimates for vertex-transitive graphs, where we obtain improved bounds which depend on the growth of the graphs. The most delicate cases are when the diameter is comparable to that of low-dimensional tori. In particular, in "dimensions" less than four (up to logarithmic factors) our error terms are the square of those of Aldous and Brown. These improved bounds play a crucial role in the companion work arXiv:2202.02255 characterising the fluctuations of the cover time on vertex-transitive graphs. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_03864 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Stationary hitting times on vertex-transitive graphs Berestycki, Nathanaël Hermon, Jonathan Teyssier, Lucas Probability 60J10 (Primary), 60J27 (Secondary) We prove a refined version of the Aldous and Brown's exponential approximation of stationary hitting times. These are valid for all reversible Markov chains. We then specialise our estimates for vertex-transitive graphs, where we obtain improved bounds which depend on the growth of the graphs. The most delicate cases are when the diameter is comparable to that of low-dimensional tori. In particular, in "dimensions" less than four (up to logarithmic factors) our error terms are the square of those of Aldous and Brown. These improved bounds play a crucial role in the companion work arXiv:2202.02255 characterising the fluctuations of the cover time on vertex-transitive graphs. |
| title | Stationary hitting times on vertex-transitive graphs |
| topic | Probability 60J10 (Primary), 60J27 (Secondary) |
| url | https://arxiv.org/abs/2601.03864 |