Abstract Understanding the statistics of collisions among locally confined gas particles poses a major challenge. In this work we investigate Zᵈ 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 p^* Zᵈ 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 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 p^* p ∗.
Bahsoun et al. (Thu,) studied this question.