High-dimensional Laplace asymptotics up to the concentration threshold

Alexander Katsevich, Anya Katsevich

We study high-dimensional Laplace-type integrals $I(\lambda ):=(\lambda /2\pi {)}^{d/2}{\int }_{{\mathbb{R}}^d}g(x)e^{-\lambda f(x)}dx$ in the regime where both $d$ and $\lambda$ are large. Existing rigorous Laplace-e…