General Limit Distributions for Sums of Random Variables with a Matrix Product Representation

2014/06/19 by Florian Angeletti, Eric Bertin, Patrice Abry
Computer Science · Mathematics · Physics and Astronomy · #Ansatz #Bayesian Methods and Mixture Models #Ergodicity #Limit (mathematics) #Markov Chains and Monte Carlo Methods #Markov chain #Markov process #Matrix (chemical analysis) #Product (mathematics) #Random Matrices and Applications #Random matrix #Random variable #Variable-order Markov model #cond-mat.stat-mech

paper · pdf · doi:10.1007/s10955-014-1111-y

published as J. Stat. Phys. (2014) 157:1255-1283 · 32 pages, 2 figure, submitted to Journal of Statistical Physics

arxiv created 2014/06/19 · openalex publication_date 2014/09/24 · arxiv updated 2014/11/24 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

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.

Citations

• Finite-dimensional representations of the quadratic algebra: Applications to the exclusion process
• Matrix product states of three families of one-dimensional interacting particle systems
• Magnetic fluctuations in the classicalXYmodel: The origin of an exponential tail in a complex system
• Active nematics on a substrate: Giant number fluctuations and long-time tails
• The random walk's guide to anomalous diffusion: a fractional dynamics approach
• Roughness distributions for1/fαsignals