Florian Angeletti

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Matrix representation, Random variables sums

General limit distributions for sums of random variables with a matrix product representation,

F. Angeletti, E. Bertin, P. Abry, Journal of Statistical Physics, (2014), 1255-1283,
doi:10.1007/s10955-014-1111-y, arxiv:1406.5016, BIB, PDF

Abstract

The general limit distributions of the sum of random variables described by a finite matrix product ansatz are characterized. Using a mapping to a Hidden Markov Chain formalism,non-standard limit distributions are obtained,and related to a form of ergodicity breaking in the underlying non-homogeneous Hidden Markov Chain. The link between ergodicity and limit distributions is detailed and used to provide a full algorithmic characterization of the general limit distributions.