WHERE DO BROWNIAN PARTICLES SPEND THEIR TIME

We study statistical properties of the fraction of time spent by a Bro wnian particle in different regions of space. Also treated in our anal ysis are the effects of one or more constraints on the trajectory at d ifferent times. We show that the effects of imposing n constraints can be analyzed in terms of the probability density of the residence time for a single constraint, An analogy to the description of the spatial density of a polymer chain is proposed and applied to evaluate the mo nomeric density in some specific examples. (C) 1998 Elsevier Science B .V. All rights reserved.