2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/76684We study the fluctuations, in the large deviations regime, of the longest increasing subsequence of a random i.i.d. sample on the unit square. In particular, our results yield the precise upper and lower exponential tails for the length of the longest increasing subsequence of a random permutation.16 pagesProbability60G70; 60F10text