On L2 modulus of continuity of Brownian local times and Riesz potentials

This article is concerned with modulus of continuity of Brownian local times.Specifically, we focus on three closely related problems:(a)Limit theorem for a Brownian modulus of continuity involving Riesz potentials, where the limit law is an intricate Gaussian mixture.(b)Central limit theorems for the projections of L2 modulus of continuity for a one-dimensional Brownian motion.(c)Extension of the second result to a two-dimensional Brownian motion.Our proofs rely on a combination of stochastic calculus and Malliavin calculus tools, plus a thorough analysis of singular integrals.