Limit theorems for sums of dependent random variables occurring in statistical mechanics

Richard S. Ellis, Charles M. Newman

Research output: Contribution to journalArticle

Abstract

We study the asymptotic behavior of partial sums Snfor certain triangular arrays of dependent, identically distributed random variables which arise naturally in statistical mechanics. A typical result is that under appropriate assumptions there exist a real number m, a positive real number λ, and a positive integer k so that (Sn-nm)/n1-1/2k converges weakly to a random variable with density proportional to exp(-λ|s|2k/(2k)!). We explain the relation of these results to topics in Gaussian quadrature, to the theory of moment spaces, and to critical phenomena in physical systems.

Original languageEnglish (US)
Pages (from-to)117-139
Number of pages23
JournalZeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
Volume44
Issue number2
DOIs
StatePublished - Jun 1978

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Dependent Random Variables
Limit Theorems
Statistical Mechanics
Random variable
Triangular Array
Gaussian Quadrature
Critical Phenomena
Partial Sums
Identically distributed
Asymptotic Behavior
Directly proportional
Moment
Converge
Integer
Dependent

ASJC Scopus subject areas

  • Statistics and Probability
  • Analysis
  • Mathematics(all)

Cite this

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