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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2210.15580 |
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| _version_ | 1866910265147129856 |
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| author | Liu, Yucheng |
| author_facet | Liu, Yucheng |
| contents | Weakly self-avoiding walk (WSAW) is a model of simple random walk paths that penalizes self-intersections. On $\mathbb{Z}$, Greven and den Hollander proved in 1993 that the discrete-time weakly self-avoiding walk has an asymptotically deterministic escape speed, and they conjectured that this speed should be strictly increasing in the repelling strength parameter. We study a continuous-time version of the model, give a different existence proof for the speed, and prove the speed to be strictly increasing. The proof uses a transfer matrix method implemented via a supersymmetric version of the BFS--Dynkin isomorphism theorem, spectral theory, Tauberian theory, and stochastic dominance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_15580 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Continuous-time weakly self-avoiding walk on $\mathbb{Z}$ has strictly monotone escape speed Liu, Yucheng Probability Mathematical Physics 60K35, 82B41 Weakly self-avoiding walk (WSAW) is a model of simple random walk paths that penalizes self-intersections. On $\mathbb{Z}$, Greven and den Hollander proved in 1993 that the discrete-time weakly self-avoiding walk has an asymptotically deterministic escape speed, and they conjectured that this speed should be strictly increasing in the repelling strength parameter. We study a continuous-time version of the model, give a different existence proof for the speed, and prove the speed to be strictly increasing. The proof uses a transfer matrix method implemented via a supersymmetric version of the BFS--Dynkin isomorphism theorem, spectral theory, Tauberian theory, and stochastic dominance. |
| title | Continuous-time weakly self-avoiding walk on $\mathbb{Z}$ has strictly monotone escape speed |
| topic | Probability Mathematical Physics 60K35, 82B41 |
| url | https://arxiv.org/abs/2210.15580 |