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.
Publié le : 1982-02-14
Classification:
Laplace's method,
Gaussian measure,
function space integral,
specific free energy,
60B11,
28C20,
82A05
@article{1176993913,
author = {Ellis, Richard S. and Rosen, Jay S.},
title = {Laplace's Method for Gaussian Integrals with an Application to Statistical Mechanics},
journal = {Ann. Probab.},
volume = {10},
number = {4},
year = {1982},
pages = { 47-66},
language = {en},
url = {http://dml.mathdoc.fr/item/1176993913}
}
Ellis, Richard S.; Rosen, Jay S. Laplace's Method for Gaussian Integrals with an Application to Statistical Mechanics. Ann. Probab., Tome 10 (1982) no. 4, pp. 47-66. http://gdmltest.u-ga.fr/item/1176993913/