2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/101101We prove an exponential approximation for the law of approximate occurrence of typical patterns for a class of Gibssian sources on the lattice $\mathbb{Z}^d$, $d\ge2$. From this result, we deduce a law of large numbers and a large deviation result for the waiting time of distorted patterns.Published at http://dx.doi.org/10.1214/105051605000000827 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)Probability60G60 (Primary) 60F05, 60F10, 94A08, 94A34 (Secondary)text