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)|
|Number of pages||23|
|Journal||Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete|
|State||Published - Jun 1978|
ASJC Scopus subject areas
- Statistics and Probability