Restrictions of some reinforced processes to subgraphs
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913575406141440 |
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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 prove that the restriction of the vertex-reinforced jump process to a subset of the vertex set is a mixture of vertex-reinforced jump processes. A similar statement holds for the non-linear hyperbolic supersymmetric sigma model. This is then applied to vertex-reinforced jump processes on subdivided versions of graphs of bounded degree, where every edge is replaced by a finite sequence of edges. We prove that discrete-time processes associated to suitable corresponding restrictions are mixtures of positive recurrent Markov chains. We also deduce a similar statement for edge-reinforced random walks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_06195 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Restrictions of some reinforced processes to subgraphs Disertori, Margherita Merkl, Franz Rolles, Silke W. W. Probability Primary 60K35, 60K37, secondary 60G60 We prove that the restriction of the vertex-reinforced jump process to a subset of the vertex set is a mixture of vertex-reinforced jump processes. A similar statement holds for the non-linear hyperbolic supersymmetric sigma model. This is then applied to vertex-reinforced jump processes on subdivided versions of graphs of bounded degree, where every edge is replaced by a finite sequence of edges. We prove that discrete-time processes associated to suitable corresponding restrictions are mixtures of positive recurrent Markov chains. We also deduce a similar statement for edge-reinforced random walks. |
| title | Restrictions of some reinforced processes to subgraphs |
| topic | Probability Primary 60K35, 60K37, secondary 60G60 |
| url | https://arxiv.org/abs/2411.06195 |