*Miguel Natalio Abadi, Liliam Cardeño*

We define the first match function Tn : C^n → {1, ... , n} where C is a finite alphabet. For two copies of x_{1}^n ∈ C^n, this function gives the minimum number of steps one has to slide one copy of x_{1}^n to get a match with the other one. For ergodic positive entropy processes, Saussol and coauthors proved the almost sure convergence of Tn/n. We compute the large deviation properties of this function. We prove that this limit is related to the Rényi entropy function, which is also proved to exist.