Superdiffusive planar random walks with polynomial space-time drifts
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929405249454080 |
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| author | da Costa, Conrado Menshikov, Mikhail Shcherbakov, Vadim Wade, Andrew |
| author_facet | da Costa, Conrado Menshikov, Mikhail Shcherbakov, Vadim Wade, Andrew |
| contents | We quantify superdiffusive transience for a two-dimensional random walk in which the vertical coordinate is a martingale and the horizontal coordinate has a positive drift that is a polynomial function of the individual coordinates and of the present time. We describe how the model was motivated through an heuristic connection to a self-interacting, planar random walk which interacts with its own centre of mass via an excluded-volume mechanism, and is conjectured to be superdiffusive with a scale exponent $3/4$. The self-interacting process originated in discussions with Francis Comets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_07813 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Superdiffusive planar random walks with polynomial space-time drifts da Costa, Conrado Menshikov, Mikhail Shcherbakov, Vadim Wade, Andrew Probability 60J10 (Primary) 60G50, 60K50, 60F05, 60F15 (Secondary) We quantify superdiffusive transience for a two-dimensional random walk in which the vertical coordinate is a martingale and the horizontal coordinate has a positive drift that is a polynomial function of the individual coordinates and of the present time. We describe how the model was motivated through an heuristic connection to a self-interacting, planar random walk which interacts with its own centre of mass via an excluded-volume mechanism, and is conjectured to be superdiffusive with a scale exponent $3/4$. The self-interacting process originated in discussions with Francis Comets. |
| title | Superdiffusive planar random walks with polynomial space-time drifts |
| topic | Probability 60J10 (Primary) 60G50, 60K50, 60F05, 60F15 (Secondary) |
| url | https://arxiv.org/abs/2401.07813 |