Year: 2026
Type: article
Abstract: Understanding the statistics of collisions among locally confined gas particles poses a major challenge. In this work we investigate $$\mathbb {Z}^d$$ 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 $${\textbf{p}}^*\in \mathbb {Z}^d$$ p ∗ ∈ 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 $${\textbf{p}}^*$$ 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 $${\textbf{p}}^*$$ p ∗ .
Authors: Wael Bahsoun, Maxence Phalempin
Institutions: Loughborough University, UNSW Sydney
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,990
OpenAlex ID: W7127935715