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

Richard S. Ellis, Charles M. Newman

Research output: Contribution to journalArticlepeer-review

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

ASJC Scopus subject areas

  • Analysis
  • Statistics and Probability
  • Mathematics(all)

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