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February, 1982 Laplace's Method for Gaussian Integrals with an Application to Statistical Mechanics
Richard S. Ellis, Jay S. Rosen
Ann. Probab. 10(1): 47-66 (February, 1982). DOI: 10.1214/aop/1176993913


For a new class of Gaussian function space integrals depending upon $n \in \{1, 2,\cdots\}$, the exponential rate of growth or decay as $n \rightarrow \infty$ is determined. The result is applied to the calculation of the specific free energy in a model in statistical mechanics. The physical discussion is self-contained. The paper ends by proving upper bounds on certain probabilities. These bounds will be used in a sequel to this paper, in which asymptotic expansions and limit theorems will be proved for the Gaussian integrals considered here.


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Richard S. Ellis. Jay S. Rosen. "Laplace's Method for Gaussian Integrals with an Application to Statistical Mechanics." Ann. Probab. 10 (1) 47 - 66, February, 1982.


Published: February, 1982
First available in Project Euclid: 19 April 2007

zbMATH: 0499.60031
MathSciNet: MR637376
Digital Object Identifier: 10.1214/aop/1176993913

Primary: 60B11
Secondary: 28C20 , 82A05

Keywords: function space integral , Gaussian measure , Laplace's method , specific free energy

Rights: Copyright © 1982 Institute of Mathematical Statistics


Vol.10 • No. 1 • February, 1982
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