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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.01337 |
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| _version_ | 1866909819618721792 |
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| author | Wang, Jinglin Zeng, Xiaolin |
| author_facet | Wang, Jinglin Zeng, Xiaolin |
| contents | We show that the vertex-reinforced jump processes on a \(d\)-dimensional hierarchical lattice are recurrent for \(d < 2\) and transient for \(d > 2\). We also explore certain regimes when \(d = 2\). The proof of recurrence relies on an exponential decay estimate of the fractional moment of the Green's function, which, unlike the classical approach used for \(\mathbb{Z}^d\), requires additional entropy estimates via stability of the model distribution under coarse grain operation, which leverages its linear reinforcement. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_01337 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Recurrence of the VRJP and Exponential Decay in the \(H^{2|2}\)-Model on the Hierarchical Lattice for \(d\le 2\) Wang, Jinglin Zeng, Xiaolin Probability Mathematical Physics 60 We show that the vertex-reinforced jump processes on a \(d\)-dimensional hierarchical lattice are recurrent for \(d < 2\) and transient for \(d > 2\). We also explore certain regimes when \(d = 2\). The proof of recurrence relies on an exponential decay estimate of the fractional moment of the Green's function, which, unlike the classical approach used for \(\mathbb{Z}^d\), requires additional entropy estimates via stability of the model distribution under coarse grain operation, which leverages its linear reinforcement. |
| title | Recurrence of the VRJP and Exponential Decay in the \(H^{2|2}\)-Model on the Hierarchical Lattice for \(d\le 2\) |
| topic | Probability Mathematical Physics 60 |
| url | https://arxiv.org/abs/2505.01337 |