## The Annals of Probability

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

#### 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