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 language | English (US) |
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Pages (from-to) | 117-139 |
Number of pages | 23 |
Journal | Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete |
Volume | 44 |
Issue number | 2 |
DOIs | |
State | Published - Jun 1978 |
ASJC Scopus subject areas
- Analysis
- Statistics and Probability
- Mathematics(all)