General limit distributions for sums of random variables with a matrix product representation
Statistical Mechanics
2014-11-24 v1
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.
Keywords
Cite
@article{arxiv.1406.5016,
title = {General limit distributions for sums of random variables with a matrix product representation},
author = {Florian Angeletti and Eric Bertin and Patrice Abry},
journal= {arXiv preprint arXiv:1406.5016},
year = {2014}
}
Comments
32 pages, 2 figure, submitted to Journal of Statistical Physics