Transience of vertex-reinforced jump processes with long-range jumps
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866911064652775424 |
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| author | Disertori, Margherita Merkl, Franz Rolles, Silke W. W. |
| author_facet | Disertori, Margherita Merkl, Franz Rolles, Silke W. W. |
| contents | We show that the vertex-reinforced jump process on the $d$-dimensional lattice with long-range jumps is transient in any dimension $d$ as long as the initial weights do not decay too fast. The main ingredients in the proof are: an analysis of the corresponding random environment on finite boxes, a comparison with a hierarchical model, and the reduction of the hierarchical model to a non-homogeneous effective one-dimensional model. For $d\ge 3$ we also prove transience of the vertex-reinforced jump process with possibly long-range jumps as long as nearest-neighbor weights are large enough. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_07359 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Transience of vertex-reinforced jump processes with long-range jumps Disertori, Margherita Merkl, Franz Rolles, Silke W. W. Probability Mathematical Physics Primary 60K35, 60K37, secondary 60G60 We show that the vertex-reinforced jump process on the $d$-dimensional lattice with long-range jumps is transient in any dimension $d$ as long as the initial weights do not decay too fast. The main ingredients in the proof are: an analysis of the corresponding random environment on finite boxes, a comparison with a hierarchical model, and the reduction of the hierarchical model to a non-homogeneous effective one-dimensional model. For $d\ge 3$ we also prove transience of the vertex-reinforced jump process with possibly long-range jumps as long as nearest-neighbor weights are large enough. |
| title | Transience of vertex-reinforced jump processes with long-range jumps |
| topic | Probability Mathematical Physics Primary 60K35, 60K37, secondary 60G60 |
| url | https://arxiv.org/abs/2305.07359 |