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

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

References in corpus (4)

• Nonequilibrium Steady States of Matrix Product Form: A Solver's Guide
• Matrix product solution of the multispecies partially asymmetric exclusion process
• Active Absorbing State Phase Transition Beyond Directed Percolation : A Class of Exactly Solvable Models
• Renormalization flow in extreme value statistics

Cited by in corpus (2)

• Matrix Product representation of the stationary state of the open Zero Range Process
• Matrix product solution of the stationary states of two-species open zero range processes