Rare events statistics for $\mathbb Z^d$ map lattices coupled by collision
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866911380923219968 |
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| author | Bahsoun, Wael Phalempin, Maxence |
| author_facet | Bahsoun, Wael Phalempin, Maxence |
| contents | Understanding the statistics of collisions among locally confined gas particles poses a major challenge. In this work we investigate $\mathbb Z^d$-map lattices coupled by collision with simplified local dynamics that offer significant insights for the above challenging problem. We obtain a first order approximation for the first collision rate at a site $\textbf{p}^*\in \mathbb Z^d$ and we prove a distributional convergence for the first collision time to an exponential, with sharp error term. Moreover, we prove that the number of collisions at site $\textbf{p}^*$ converge in distribution to a compound Poisson distributed random variable. Key to our analysis in this infinite dimensional setting is the use of transfer operators associated with the decoupled map lattice at site $\textbf{p}^*$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_12803 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Rare events statistics for $\mathbb Z^d$ map lattices coupled by collision Bahsoun, Wael Phalempin, Maxence Dynamical Systems Probability Understanding the statistics of collisions among locally confined gas particles poses a major challenge. In this work we investigate $\mathbb Z^d$-map lattices coupled by collision with simplified local dynamics that offer significant insights for the above challenging problem. We obtain a first order approximation for the first collision rate at a site $\textbf{p}^*\in \mathbb Z^d$ and we prove a distributional convergence for the first collision time to an exponential, with sharp error term. Moreover, we prove that the number of collisions at site $\textbf{p}^*$ converge in distribution to a compound Poisson distributed random variable. Key to our analysis in this infinite dimensional setting is the use of transfer operators associated with the decoupled map lattice at site $\textbf{p}^*$. |
| title | Rare events statistics for $\mathbb Z^d$ map lattices coupled by collision |
| topic | Dynamical Systems Probability |
| url | https://arxiv.org/abs/2412.12803 |