On the return probability of the simple random walk on Galton-Watson trees
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929681166499840 |
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| author | Müller, Peter Stern, Jakob |
| author_facet | Müller, Peter Stern, Jakob |
| contents | We consider the simple random walk on Galton-Watson trees with supercritical offspring distribution, conditioned on non-extinction. In case the offspring distribution has finite support, we prove an upper bound for the annealed return probability to the root which decays subexponentially in time with exponent 1/3. This exponent is optimal. Our result improves the previously known subexponential upper bound with exponent 1/5 by Piau [Ann. Probab. 26, 1016-1040 (1998)]. For offspring distributions with unbounded support but sufficiently fast decay, our method also yields improved subexponential upper bounds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_01600 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the return probability of the simple random walk on Galton-Watson trees Müller, Peter Stern, Jakob Probability Mathematical Physics 05C81, 60K37, 60J80 We consider the simple random walk on Galton-Watson trees with supercritical offspring distribution, conditioned on non-extinction. In case the offspring distribution has finite support, we prove an upper bound for the annealed return probability to the root which decays subexponentially in time with exponent 1/3. This exponent is optimal. Our result improves the previously known subexponential upper bound with exponent 1/5 by Piau [Ann. Probab. 26, 1016-1040 (1998)]. For offspring distributions with unbounded support but sufficiently fast decay, our method also yields improved subexponential upper bounds. |
| title | On the return probability of the simple random walk on Galton-Watson trees |
| topic | Probability Mathematical Physics 05C81, 60K37, 60J80 |
| url | https://arxiv.org/abs/2402.01600 |