2022/10/20 by Arturo Jaramillo, Jaramillo, Arturo, James Melbourne +1 · 1 citation
Mathematics · #Point processes and geometric inequalities #Random Matrices and Applications #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.2210.11632
In this paper we develop tools for studying limit theorems by means of convexity. We establish bounds for the discrepancy in total variation between probability measures μ and ν such that ν is log-concave with respect to μ. We discuss a variety of applications, which include geometric and binomial approximations to sums of random variables, and discrepancy between Gamma distributions. As special cases we obtain a law of rare events for intrinsic volumes, quantitative bounds on proximity to geometric for infinitely divisible distributions, as well as binomial and Poisson approximation for matroids.