Inverting Ray-Knight identities on trees
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866909276617834496 |
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| author | Li, Xiaodan Zheng, Yushu |
| author_facet | Li, Xiaodan Zheng, Yushu |
| contents | In this paper, we first introduce the Ray-Knight identity and percolation Ray-Knight identity related to loop soup with intensity $α(\ge 0)$ on trees. Then we present the inversions of the above identities, which are expressed in terms of repelling jump processes. In particular, the inversion in the case of $α=0$ gives the conditional law of a Markov jump process given its local time field. We further show that the fine mesh limits of these repelling jump processes are the self-repelling diffusions \cite{Aidekon} involved in the inversion of the Ray-Knight identity on the corresponding metric graph. This is a generalization of results in \cite{2016Inverting,lupu2019inverting,LupuEJP657}, where the authors explore the case of $α=1/2$ on a general graph. Our construction is different from \cite{2016Inverting,lupu2019inverting} and based on the link between random networks and loop soups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_02966 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Inverting Ray-Knight identities on trees Li, Xiaodan Zheng, Yushu Probability Primary 60K35, 60J55, Secondary 60G55, 60J27, 60J65 In this paper, we first introduce the Ray-Knight identity and percolation Ray-Knight identity related to loop soup with intensity $α(\ge 0)$ on trees. Then we present the inversions of the above identities, which are expressed in terms of repelling jump processes. In particular, the inversion in the case of $α=0$ gives the conditional law of a Markov jump process given its local time field. We further show that the fine mesh limits of these repelling jump processes are the self-repelling diffusions \cite{Aidekon} involved in the inversion of the Ray-Knight identity on the corresponding metric graph. This is a generalization of results in \cite{2016Inverting,lupu2019inverting,LupuEJP657}, where the authors explore the case of $α=1/2$ on a general graph. Our construction is different from \cite{2016Inverting,lupu2019inverting} and based on the link between random networks and loop soups. |
| title | Inverting Ray-Knight identities on trees |
| topic | Probability Primary 60K35, 60J55, Secondary 60G55, 60J27, 60J65 |
| url | https://arxiv.org/abs/2206.02966 |