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.
Citation
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. https://doi.org/10.1214/aop/1176993913
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