Limit theorems for sums of dependent random variables occurring in statistical mechanics |
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| Authors: | Richard S. Ellis Charles M. Newman Jay S. Rosen |
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| Affiliation: | (1) Department of Mathematics and Statistics, University of Massachusetts, 01003 Amherst, Massachusetts, USA;(2) Department of Mathematics, Indiana University, 47401 Bloomington, Indiana, USA;(3) Department of Mathematics and Statistics, University of Massachusetts, 01003 Amherst, Massachusetts, USA;(4) Present address: Department of Mathematics, University of Arizona, 85721 Tucson, Arizona, USA |
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| Abstract: | Summary By the use of conditioning, we extend previously obtained results on the asymptotic behavior of partial sums for certain triangular arrays of dependent random variables, known as Curie-Weiss models. These models arise naturally in statistical mechanics. The relation of these results to multiple phases, metastable states, and other physical phenomena is explained.Alfred P. Sloan Research Fellow. Research supported in part by National Science Foundation Grant MPS 76-06644A01Alfred P. Sloan Research Fellow. Research supported in part by National Science Foundation Grant MCS 77-20683 and by U.S.-Israel Binational Science FoundationResearch supported in part by National Science Foundation Grant PHY77-02172 |
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