LAPLACES METHOD FOR GAUSSIAN INTEGRALS WITH AN APPLICATION TO STATISTICAL-MECHANICS
Publication Date
1982
Journal or Book Title
ANNALS OF PROBABILITY
Abstract
For a new class of Gaussian function space integrals depending upon n ∈ {1, 2,⋯}, the exponential rate of growth or decay as n → ∞ 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.
Pages
47-66
Volume
10
Issue
1
Recommended Citation
Ellis, RS and ROSEN, JS, "LAPLACES METHOD FOR GAUSSIAN INTEGRALS WITH AN APPLICATION TO STATISTICAL-MECHANICS" (1982). ANNALS OF PROBABILITY. 359.
Retrieved from https://scholarworks.umass.edu/math_faculty_pubs/359
Comments
The published version is located at http://www.jstor.org/stable/2243771