The Annals of Probability

Laplace's Method for Gaussian Integrals with an Application to Statistical Mechanics

Richard S. Ellis and Jay S. Rosen

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Abstract

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.

Article information

Source
Ann. Probab., Volume 10, Number 1 (1982), 47-66.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176993913

Digital Object Identifier
doi:10.1214/aop/1176993913

Mathematical Reviews number (MathSciNet)
MR637376

Zentralblatt MATH identifier
0499.60031

JSTOR
links.jstor.org

Subjects
Primary: 60B11: Probability theory on linear topological spaces [See also 28C20]
Secondary: 28C20: Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) [See also 46G12, 58C35, 58D20, 60B11] 82A05

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

Citation

Ellis, Richard S.; Rosen, Jay S. Laplace's Method for Gaussian Integrals with an Application to Statistical Mechanics. Ann. Probab. 10 (1982), no. 1, 47--66. doi:10.1214/aop/1176993913. https://projecteuclid.org/euclid.aop/1176993913


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Corrections

  • See Correction: Richard S. Ellis, Jay S. Rosen. Correction: Correction to "Laplace's Method for Gaussian Integrals with an Application to Statistical Mechanics". Ann. Probab., Volume 11, Number 2 (1983), 456--456.