The two investigators will continue their studies in aspects of Brownian motion. Topics will include Brownian motion and the boundary behavior of harmonic functions, reflecting Brownian motion with variable angle of reflections, the Brownian convex hull, behavior of Brownian paths on the boundary of a domain, the non-Markovian side of Brownian motions, and Brownian motion on fractals. An additional topic of self-avoiding random walk will be studied. The two investigators will continue their studies in aspects of Brownian motion. Brownian motion is a specific stochastic process which is studied in probability theory. This study will impact areas of mathematics outside probability, namely potential theory and mathematical physics.
