Asymptotics of Gaussian integrals in infinite dimensions
Sergio A Albeverio, Victoria Steblovskaya · Infinite Dimensional Analysis Quantum Probability and Related Topics · 2019
We introduce an infinite-dimensional version of the classical Laplace method, in its original form, relative to a canonical Gaussian measure associated with a Hilbert space, and for a general phase function. Particular attention is given to the case of a phase function with finite-dimensional degeneracy. Explicit results on expansions in the form of power series in the relevant parameter, with estimates on remainders, are provided.