  This article resumes the analysis of precise Laplace asymptotics for the
generalised Parabolic Anderson Model (gPAM) initiated by Peter Friz and the
author. More precisely, we provide an explicit formula for the constant
coefficient in the asymptotic expansion in terms of traces and
Carleman-Fredholm determinants of certain explicit operators. The proof
combines classical Gaussian analysis in abstract Wiener spaces with arguments
from the theory of regularity structures. As an ingredient, we prove that the
minimiser in the (extended) phase functional of gPAM has better than just
Cameron-Martin regularity.
