Maximal Entropy Random Walks in Z: Random and non-random environments
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866917094600212480 |
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| author | Thibaut, Duboux Gerin, Lucas Offret, Yoann |
| author_facet | Thibaut, Duboux Gerin, Lucas Offret, Yoann |
| contents | The Maximal Entropy Random Walk (MERW) is a natural process on a finite graph, introduced a few years ago with motivations from theoretical physics. The construction of this process relies on Perron-Frobenius theory for adjacency matrices. Generalizing to infinite graphs is rather delicate, and in this article, we treat in a fairly exhaustive manner the case of the MERW on Z with loops, for both random and nonrandom loops. Thanks to an explicit combinatorial representation of the corresponding Perron-Frobenius eigenvectors, we are able to precisely determine the asymptotic behavior of these walks. We show, in particular, that essentially all MERWs on Z with loops have positive speed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_15957 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Maximal Entropy Random Walks in Z: Random and non-random environments Thibaut, Duboux Gerin, Lucas Offret, Yoann Combinatorics Probability The Maximal Entropy Random Walk (MERW) is a natural process on a finite graph, introduced a few years ago with motivations from theoretical physics. The construction of this process relies on Perron-Frobenius theory for adjacency matrices. Generalizing to infinite graphs is rather delicate, and in this article, we treat in a fairly exhaustive manner the case of the MERW on Z with loops, for both random and nonrandom loops. Thanks to an explicit combinatorial representation of the corresponding Perron-Frobenius eigenvectors, we are able to precisely determine the asymptotic behavior of these walks. We show, in particular, that essentially all MERWs on Z with loops have positive speed. |
| title | Maximal Entropy Random Walks in Z: Random and non-random environments |
| topic | Combinatorics Probability |
| url | https://arxiv.org/abs/2503.15957 |