Rényi Entropies and Large Deviations for the First Match Function

Speaker: Miguel Abadi - IME-USP
Date: Mar 19, 2015
Time: 14h00
Local: Numec´s multipurpose room

Abstract: We define the first match function Tn : Cn → {1,...,n} where C is a finite alphabet. For two copies of x1n ∈ Cn, this function gives the minimum number of steps one has to slide one copy of x1n 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. Our results hold under a condition easy to check which defines a large class of processes. We provide some examples.

 

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