  Many dynamics are random processes with increments given by a quadratic form
of a fast Gaussian process. We find that the rate function which describes path
large deviations can be computed from the large interval asymptotic of a
certain Fredholm determinant. The latter can be evaluated explicitly using
Widom's theorem which generalizes the celebrated Szego-Kac formula to the
multi-dimensional case. This provides a large class of dynamics with explicit
path large deviation functionals. Inspired by problems in hydrodynamics and
atmosphere dynamics, we present the simplest example of the emergence of
metastability for such a process.
