  This article is concerned with modulus of continuity of Brownian local times.
Specifically, we focus on 3 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 1-dimensional Brownian motion.
(c) Extension of the second result to a 2-dimensional Brownian motion. Our
proofs rely on a combination of stochastic calculus and Malliavin calculus
tools, plus a thorough analysis of singular integrals.
