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arXiv · 2412.12803

Rare events statistics for $\mathbb Z^d$ map lattices coupled by collision

Wael Bahsoun·Maxence Phalempin
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Abstract

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 $\textbf{p}^*$.

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Wael Bahsoun, Maxence Phalempin. 2024-12-17. Rare events statistics for $\mathbb Z^d$ map lattices coupled by collision. https://arxiv.org/abs/2412.12803

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