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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/2503.04503 |
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| _version_ | 1866909956823842816 |
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| author | Chang, Yinshan Huang, Yichao Liu, Dang-Zheng Zeng, Xiaolin |
| author_facet | Chang, Yinshan Huang, Yichao Liu, Dang-Zheng Zeng, Xiaolin |
| contents | The goal of this note is twofold: first, we explain the relation between the isomorphism theorems in the context of vertex reinforced jump process discovered in [BHS19, BHS21] and the standard Markovian isomorphism theorems for Markovian jump processes; second, we introduce the vertex reinforced counterpart of the standard Poissonian loop soup developed by Le Jan [LJ10]. To this end, we propose an algorithm that can be viewed as a variant of Wilson's algorithm with reinforcement. We establish the isomorphism theorems for the erased loops and the random walk from this algorithm, and in particular provide a concrete construction of the reinforced loop soup via a random process with a reinforcement mechanism. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_04503 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Reinforced Loop Soup via Wilson's Algorithm Chang, Yinshan Huang, Yichao Liu, Dang-Zheng Zeng, Xiaolin Probability Mathematical Physics The goal of this note is twofold: first, we explain the relation between the isomorphism theorems in the context of vertex reinforced jump process discovered in [BHS19, BHS21] and the standard Markovian isomorphism theorems for Markovian jump processes; second, we introduce the vertex reinforced counterpart of the standard Poissonian loop soup developed by Le Jan [LJ10]. To this end, we propose an algorithm that can be viewed as a variant of Wilson's algorithm with reinforcement. We establish the isomorphism theorems for the erased loops and the random walk from this algorithm, and in particular provide a concrete construction of the reinforced loop soup via a random process with a reinforcement mechanism. |
| title | Reinforced Loop Soup via Wilson's Algorithm |
| topic | Probability Mathematical Physics |
| url | https://arxiv.org/abs/2503.04503 |