This paper considers expectations of the form $E\exp \left\{\sum_{i=1}^m \phi_i \right\}$, where $\phi_i: {\Bbb R}^n \longrightarrow {\Bbb C}$ are functions depending on a few coordinates of a point in ${\Bbb R}^n$. The expectation is taken with respect to standard Gaussian or symmetric exponential probability measures. We prove sufficient conditions concerning the Lipschitz constants of $\phi_i$ and the combinatorics of their dependencies for the integral to be non-zero, thus making it amenable to computationally efficient approximation. Applications to computing volumes of bodies and statistics on integer points in polyhedra in ${\Bbb R}^n$ are also discussed.
Blogger's Review: This paper provides a fresh perspective on integral computation under high-dimensional probability measures, emphasizing the role of Lipschitz constants, with significant practical implications in geometric and statistical problems, showcasing broad potential for real-world applications.