Burgess Davis

Reinforced random walk

SummaryLetai,i≧1, be a sequence of nonnegative numbers. Difine a nearest neighbor random motion

On the weak type (1,1) inequality for conjugate functions

\overrightarrow X

A Geometric Condition that Implies the Existence of Certain Singular Integrals of Banach-Space-Valued Functions

=X0,X1, ... on the integers as follows. Initially the weight of each interval (i, i+1), i an integer, equals 1. If at timen an interval (i, i+1) has been crossed exactlyk times by the motion, its weight is

On Brownian slow points

1 + \sum\limits_{j = 1}^k {a_j }

On the spectral gap for fixed membranes

. Given (X0,X1, ...,Xn)=(i0, i1, ..., in), the probability thatXn+1 isin−1 orin+1 is proportional to the weights at timen of the intervals (in−1,in) and (in,iin+1). We prove that