Diffusion of the random Lorentz process in a magnetic field
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913572817207296 |
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| author | Lutsko, Christopher Toth, Balint |
| author_facet | Lutsko, Christopher Toth, Balint |
| contents | Consider the motion of a charged, point particle moving in the complement of a Poisson distribution of hard sphere scatterers in two dimensions under the effect of a fixed magnetic field. Building on, and extending a coupling method established by the authors, we show that this 'magnetic Lorentz gas' satisfies an invariance principle in an intermediate scaling limit. That is, we apply the low-density (Boltzmann-Grad) limit and simultaneously take the limit as time goes to infinity, then prove convergence of the rescaled trajectory to a Brownian motion in this limit. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_03984 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Diffusion of the random Lorentz process in a magnetic field Lutsko, Christopher Toth, Balint Probability Mathematical Physics 60F17, 60K35, 82C22 Consider the motion of a charged, point particle moving in the complement of a Poisson distribution of hard sphere scatterers in two dimensions under the effect of a fixed magnetic field. Building on, and extending a coupling method established by the authors, we show that this 'magnetic Lorentz gas' satisfies an invariance principle in an intermediate scaling limit. That is, we apply the low-density (Boltzmann-Grad) limit and simultaneously take the limit as time goes to infinity, then prove convergence of the rescaled trajectory to a Brownian motion in this limit. |
| title | Diffusion of the random Lorentz process in a magnetic field |
| topic | Probability Mathematical Physics 60F17, 60K35, 82C22 |
| url | https://arxiv.org/abs/2411.03984 |