General limit distributions for sums of random variables with a matrix product representation
arXiv:1406.5016 · doi:10.1007/s10955-014-1111-y
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.
32 pages, 2 figure, submitted to Journal of Statistical Physics