ILLINOIS JOURNAL OF MATHEMATICS Volume 50, Number 1 Spring 2006
Foreword v Donald Burkholder, Joseph Leo Doob (1910-2004) vii Rodrigo Banuelos and Pedro J. Mendez-Hernandez. Hot spots for
conditioned Brownian motion 1 Martin T. Barlow and Takashi Kumagai, Random walk on the incipient
infinite cluster on trees 33 Federico Bassetti and Persi Diaconis, Examples comparing importance
sampling and the Metropolis algorithm 67 Robert O. Bauer and Roland M. Friedrich, Diffusing polygons and
SLE ... 93
Istvan Berkes, Walter Philipp and Robert F. Tichy, Empirical processes
in probabilistic number theory: the LIL for the discrepancy of ( mod 1 107 Jean Bertoin and Jean-Frangois Le Gall. Stochastic flows associated to
coalescent processes III: Limit theorems 147 Jean Bourgain, Nonlinear Schrodinger equation with a random potential 183 Krzysztof Burdzy, Zhen-Qing Chen and Peter Jones, Synchronous
couplings of reflected Brownian motions in smooth domains 189
