Geometry-induced criticality in $p$-adic scaling limits of random walks
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909814443999232 |
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| author | Rajkumar, Rahul Weisbart, David |
| author_facet | Rajkumar, Rahul Weisbart, David |
| contents | An anisotropy parameter $h$ in $(0,1]$ induces on $\mathbb{Q}_p^2$ a duality-compatible, two-scale filtration that collapses to one scale at the right endpoint. This filtration defines shell-uniform transition laws for hierarchical random walks on a discrete group whose scaling limits are Lévy processes on $\mathbb{Q}_p^2$. The diffusion constants of the coordinate processes jump at the right endpoint, even though the radial jump law depends continuously on $h$. This instance of geometry-induced criticality isolates a structural mechanism that should extend to locally compact abelian groups and suggests a route to studying critical behavior in ultrametric models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_24234 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Geometry-induced criticality in $p$-adic scaling limits of random walks Rajkumar, Rahul Weisbart, David Probability Mathematical Physics 60F17 An anisotropy parameter $h$ in $(0,1]$ induces on $\mathbb{Q}_p^2$ a duality-compatible, two-scale filtration that collapses to one scale at the right endpoint. This filtration defines shell-uniform transition laws for hierarchical random walks on a discrete group whose scaling limits are Lévy processes on $\mathbb{Q}_p^2$. The diffusion constants of the coordinate processes jump at the right endpoint, even though the radial jump law depends continuously on $h$. This instance of geometry-induced criticality isolates a structural mechanism that should extend to locally compact abelian groups and suggests a route to studying critical behavior in ultrametric models. |
| title | Geometry-induced criticality in $p$-adic scaling limits of random walks |
| topic | Probability Mathematical Physics 60F17 |
| url | https://arxiv.org/abs/2509.24234 |