Speed of Random Walks in Dirichlet Environment on a Galton-Watson Tree
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913356968886272 |
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| author | Qian, Dongjian Xiao, Yang |
| author_facet | Qian, Dongjian Xiao, Yang |
| contents | This paper deals with a transient random walk in Dirichlet environment, or equivalently a linearly edge reinforced random walk, on a Galton-Watson tree. We compute the stationary distribution of the environment seen from the particle of an edge reinforced random walk. We obtain a formula for the speed and give a necessary and sufficient condition for the walk to have a positive speed under some moment conditions on the offspring distribution of the tree. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_11845 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Speed of Random Walks in Dirichlet Environment on a Galton-Watson Tree Qian, Dongjian Xiao, Yang Probability 60K37, 60K35, 60J80, 60F15 This paper deals with a transient random walk in Dirichlet environment, or equivalently a linearly edge reinforced random walk, on a Galton-Watson tree. We compute the stationary distribution of the environment seen from the particle of an edge reinforced random walk. We obtain a formula for the speed and give a necessary and sufficient condition for the walk to have a positive speed under some moment conditions on the offspring distribution of the tree. |
| title | Speed of Random Walks in Dirichlet Environment on a Galton-Watson Tree |
| topic | Probability 60K37, 60K35, 60J80, 60F15 |
| url | https://arxiv.org/abs/2405.11845 |