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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.08158 |
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| _version_ | 1866912491149197312 |
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| author | Li, Songzi |
| author_facet | Li, Songzi |
| contents | We study the periodic Lorentz gas in the Boltzmann-Grad limit, whose convergence was rigorously established in the seminal work of Marklof-Strömbergsson. Extending the two dimensional results of Boca-Zaharescu to higher dimensions, we present a more detailed description of this convergence. More precisely, we derive the asymptotic formula of the distribution function of the free path length; and we explicitly compute the constant in the asymptotic formula for the Kolmogorov-Sinai (K-S) entropy of the billiard map. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_08158 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The periodic Lorentz gas in the Boltzmann-Grad limit: the free path length and the K-S entropy Li, Songzi Probability We study the periodic Lorentz gas in the Boltzmann-Grad limit, whose convergence was rigorously established in the seminal work of Marklof-Strömbergsson. Extending the two dimensional results of Boca-Zaharescu to higher dimensions, we present a more detailed description of this convergence. More precisely, we derive the asymptotic formula of the distribution function of the free path length; and we explicitly compute the constant in the asymptotic formula for the Kolmogorov-Sinai (K-S) entropy of the billiard map. |
| title | The periodic Lorentz gas in the Boltzmann-Grad limit: the free path length and the K-S entropy |
| topic | Probability |
| url | https://arxiv.org/abs/2401.08158 |