Recent results on the asymptotic distribution of winding and crossing numbers are presented as part of a larger framework of asymptotic laws for planar Brownian motion. The approach is via random time changes, martingale calculus, and excursion theory.
"Asymptotic Laws of Planar Brownian Motion." Ann. Probab. 14 (3) 733 - 779, July, 1986. https://doi.org/10.1214/aop/1176992436