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Math. Phys."],"published-print":{"date-parts":[[2026,3]]},"abstract":"Abstract<\/jats:title>\n \n Understanding the statistics of collisions among locally confined gas particles poses a major challenge. In this work we investigate\n \n \n $$\\mathbb {Z}^d$$<\/jats:tex-math>\n \n \n \n Z<\/mml:mi>\n <\/mml:mrow>\n d<\/mml:mi>\n <\/mml:msup>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n -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\n \n \n $${\\textbf{p}}^*\\in \\mathbb {Z}^d$$<\/jats:tex-math>\n \n \n \n \n p<\/mml:mi>\n <\/mml:mrow>\n \u2217<\/mml:mo>\n <\/mml:msup>\n \u2208<\/mml:mo>\n \n \n Z<\/mml:mi>\n <\/mml:mrow>\n d<\/mml:mi>\n <\/mml:msup>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n 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\n \n \n $${\\textbf{p}}^*$$<\/jats:tex-math>\n \n \n \n p<\/mml:mi>\n <\/mml:mrow>\n \u2217<\/mml:mo>\n <\/mml:msup>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n 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\n decoupled<\/jats:italic>\n map lattice at site\n \n \n $${\\textbf{p}}^*$$<\/jats:tex-math>\n \n \n \n p<\/mml:mi>\n <\/mml:mrow>\n \u2217<\/mml:mo>\n <\/mml:msup>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n .\n <\/jats:p>","DOI":"10.1007\/s00220-026-05557-w","type":"journal-article","created":{"date-parts":[[2026,2,5]],"date-time":"2026-02-05T18:28:59Z","timestamp":1770316139000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Rare Events Statistics for $$\\mathbb {Z}^d$$ Map Lattices Coupled by Collision"],"prefix":"10.1007","volume":"407","author":[{"given":"Wael","family":"Bahsoun","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Maxence","family":"Phalempin","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,2,5]]},"reference":[{"issue":"8","key":"5557_CR1","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6544\/adfa62","volume":"38","author":"J Atnip","year":"2025","unstructured":"Atnip, J., Froyland, G., Gonz\u00e1lez-Tokman, C., Vaienti, S.: Compound Poisson statistics for dynamical systems via spectral perturbation. 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