Non-Gaussian fluctuations of randomly trapped random walks
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2018
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866909989039243264 |
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| author | Bowditch, Adam |
| author_facet | Bowditch, Adam |
| contents | In this paper we consider the one-dimensional, biased, randomly trapped random walk when the trapping times have infinite variance. We prove sufficient conditions for the suitably scaled walk to converge to a transformation of a stable Lévy process. As our main motivation, we apply subsequential versions of our results to biased walks on subcritical Galton-Watson trees conditioned to survive. This confirms the correct order of the fluctuations of the walk around its speed for values of the bias that yield a non-Gaussian regime. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1812_02369 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Non-Gaussian fluctuations of randomly trapped random walks Bowditch, Adam Probability In this paper we consider the one-dimensional, biased, randomly trapped random walk when the trapping times have infinite variance. We prove sufficient conditions for the suitably scaled walk to converge to a transformation of a stable Lévy process. As our main motivation, we apply subsequential versions of our results to biased walks on subcritical Galton-Watson trees conditioned to survive. This confirms the correct order of the fluctuations of the walk around its speed for values of the bias that yield a non-Gaussian regime. |
| title | Non-Gaussian fluctuations of randomly trapped random walks |
| topic | Probability |
| url | https://arxiv.org/abs/1812.02369 |