Probing microscopic origins of confined subdiffusion by first-passage observables

Subdiffusive motion of tracer particles in complex crowded environments, such as biological cells, has been shown to be widepsread. This deviation from brownian motion is usually characterized by a sublinear time dependence of the mean square displacement (MSD). However, subdiffusive behavior can stem from different microscopic scenarios, which can not be identified solely by the MSD data. In this paper we present a theoretical framework which permits to calculate analytically first-passage observables (mean first-passage times, splitting probabilities and occupation times distributions) in disordered media in any dimensions. This analysis is applied to two representative microscopic models of subdiffusion: continuous-time random walks with heavy tailed waiting times, and diffusion on fractals. Our results show that first-passage observables provide tools to unambiguously discriminate between the two possible microscopic scenarios of subdiffusion. Moreover we suggest experiments based on first-passage observables which could help in determining the origin of subdiffusion in complex media such as living cells, and discuss the implications of anomalous transport to reaction kinetics in cells.Comment: 21 pages, 3 figures. Submitted versio

On the joint residence time of N independent two-dimensional Brownian motions

We study the behavior of several joint residence times of N independent Brownian particles in a disc of radius $R$ in two dimensions. We consider: (i) the time T_N(t) spent by all N particles simultaneously in the disc within the time interval [0,t]; (ii) the time T_N^{(m)}(t) which at least m out of N particles spend together in the disc within the time interval [0,t]; and (iii) the time {\tilde T}_N^{(m)}(t) which exactly m out of N particles spend together in the disc within the time interval [0,t]. We obtain very simple exact expressions for the expectations of these three residence times in the limit t\to\infty.Comment: 8 page