Tail distributions of cover times of once-reinforced random walks
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913826784411648 |
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| author | Huang, Xiangyu Liu, Yong Xiang, Kainan |
| author_facet | Huang, Xiangyu Liu, Yong Xiang, Kainan |
| contents | We consider the tail distribution of the edge cover time of a specific non-Markov process, $δ$ once-reinforced random walk, on finite connected graphs, whose transition probability is proportional to weights of edges. Here the weights are $1$ on edges not traversed and $δ\in(0,\infty)$ otherwise. In detail, we show that its tail distribution decays exponentially, and obtain a phase transition of the exponential integrability of the edge cover time with critical exponent $α_c^1(δ)$, which has a variational representation and some interesting analytic properties including $α_c^1(0+)$ reflecting the graph structures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_05284 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Tail distributions of cover times of once-reinforced random walks Huang, Xiangyu Liu, Yong Xiang, Kainan Probability We consider the tail distribution of the edge cover time of a specific non-Markov process, $δ$ once-reinforced random walk, on finite connected graphs, whose transition probability is proportional to weights of edges. Here the weights are $1$ on edges not traversed and $δ\in(0,\infty)$ otherwise. In detail, we show that its tail distribution decays exponentially, and obtain a phase transition of the exponential integrability of the edge cover time with critical exponent $α_c^1(δ)$, which has a variational representation and some interesting analytic properties including $α_c^1(0+)$ reflecting the graph structures. |
| title | Tail distributions of cover times of once-reinforced random walks |
| topic | Probability |
| url | https://arxiv.org/abs/2505.05284 |