Scaling limit of the random walk on a Galton-Watson tree with regular varying offspring distribution
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866916175875670016 |
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| author | Qian, Dongjian Xiao, Yang |
| author_facet | Qian, Dongjian Xiao, Yang |
| contents | We consider a random walk on a Galton-Watson tree whose offspring distribution has a regular varying tail of order $κ\in (1,2)$. We prove the convergence of the renormalised height function of the walk towards the continuous-time height process of a spectrally positive strictly stable Lévy process, jointly with the convergence of the renormalised trace of the walk towards the continuum tree coded by the latter continuous-time height process. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_09200 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Scaling limit of the random walk on a Galton-Watson tree with regular varying offspring distribution Qian, Dongjian Xiao, Yang Probability 60J80, 60G50, 60F17 We consider a random walk on a Galton-Watson tree whose offspring distribution has a regular varying tail of order $κ\in (1,2)$. We prove the convergence of the renormalised height function of the walk towards the continuous-time height process of a spectrally positive strictly stable Lévy process, jointly with the convergence of the renormalised trace of the walk towards the continuum tree coded by the latter continuous-time height process. |
| title | Scaling limit of the random walk on a Galton-Watson tree with regular varying offspring distribution |
| topic | Probability 60J80, 60G50, 60F17 |
| url | https://arxiv.org/abs/2309.09200 |