First-passage times in confined geometrys

How long does it take a random walker to reach a given target point? This quantity, known as a first passage time (FPT), has led to a growing number of theoretical investigations over the last decade. The importance of FPTs originates from the crucial role played by first encounter properties in various real situations, including transport in disordered media, spreading of diseases or target search processes. Most methods to determine the FPT properties in confining domains have been limited to effective 1D geometries, or for space dimensions larger than one only to homogeneous media. I will propose here a general theory which allows one to evaluate the mean FPT (MFPT) in complex media. This analytical approach provides a universal scaling dependence of the MFPT on both the volume of the confining domain and the source-target distance. This analysis is applicable to representative models of transport in disordered media, fractals, and anomalous diffusion.