On approximate pattern matching for a class of Gibbs random fields

Abstract

We prove an exponential approximation for the law of approximate occurrence of typical patterns for a class of Gibssian sources on the lattice ${\mathbb{Z}}^d$, $d\ge 2$. 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)