... shallreplace Xtby the planar Brownian motion Bt= i(Xt). It follows from radialsymmetry and the strong Markov property of Brownian motion that ¯qnis in-dependent of x ∈ S. By Brownian scaling, ¯qnis ... Cover times for Brownian motionand random walks in two dimensions By Amir Dembo, Yuval Peres, Jay Rosen, and Ofer Zeitouni COVER TIMES FOR PLANAR BROWNIAN MOTION AND RANDOM WALKS451With ... the planar Brownian motion Btstarting atany z ∈ ∂D(x, εn,k) will hit ∂D(x, εn,k−1) prior to hitting ∂D(x, εn,k+1), with(Yl−1,Yl) recording the order of excursions the Brownian path...