Random walks that avoid their past convex hull
  We introduce planar random walk conditioned to avoid its past convex hull, and we show that it escapes at a positive limsup speed. Experimental results show that fluctuations from a limiting direction are on the order of n^(3/4). This behavior is also observed for the extremal investor, a natural financial model related to the planar walk. 
Omer Angel, Itai Benjamini, Balint Virag