Asymptotic direction of a ballistic random walk in a two-dimensional random environment with nonuniform mixing
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866909222649724928 |
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| author | Allasia, Julien |
| author_facet | Allasia, Julien |
| contents | In this paper, we study random walks evolving with a directional bias in a two-dimensional random environment with correlations that vanish polynomially. Using renormalization methods first employed for one-dimensional dynamic environments along with additional ideas specific to this new framework, we show that there exists an asymptotic direction for such a random walk. We also provide examples of classical models for which our results apply. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_01603 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Asymptotic direction of a ballistic random walk in a two-dimensional random environment with nonuniform mixing Allasia, Julien Probability In this paper, we study random walks evolving with a directional bias in a two-dimensional random environment with correlations that vanish polynomially. Using renormalization methods first employed for one-dimensional dynamic environments along with additional ideas specific to this new framework, we show that there exists an asymptotic direction for such a random walk. We also provide examples of classical models for which our results apply. |
| title | Asymptotic direction of a ballistic random walk in a two-dimensional random environment with nonuniform mixing |
| topic | Probability |
| url | https://arxiv.org/abs/2307.01603 |