On Anti-Confinement Estimates for Self-Repelling Random Walks
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866918340248731648 |
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| author | Schmidt, Tobias Sellke, Mark |
| author_facet | Schmidt, Tobias Sellke, Mark |
| contents | We study a class of $d$-dimensional random walks, including the two-dimensional simple random walk, reweighted by a self-repelling Gibbsian pair potential. We prove lower bounds on the diffusion constant for short-range interactions, and superdiffusive behavior in case the interaction is sufficiently long-range. Finally, we show that in the superdiffusive regime, faster temporal decay can be compensated by stronger spatial repulsion and vice-versa. Our technique combines GKS-based correlation inequalities on path space with recursive multi-scale estimates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_14497 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On Anti-Confinement Estimates for Self-Repelling Random Walks Schmidt, Tobias Sellke, Mark Probability 60K35, 82B41 We study a class of $d$-dimensional random walks, including the two-dimensional simple random walk, reweighted by a self-repelling Gibbsian pair potential. We prove lower bounds on the diffusion constant for short-range interactions, and superdiffusive behavior in case the interaction is sufficiently long-range. Finally, we show that in the superdiffusive regime, faster temporal decay can be compensated by stronger spatial repulsion and vice-versa. Our technique combines GKS-based correlation inequalities on path space with recursive multi-scale estimates. |
| title | On Anti-Confinement Estimates for Self-Repelling Random Walks |
| topic | Probability 60K35, 82B41 |
| url | https://arxiv.org/abs/2602.14497 |