Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2007-11-05
Nature 450, 77 (2007)
Physics
Condensed Matter
Statistical Mechanics
Submitted version. Supplementary Informations available on Nature website
Scientific paper
10.1038/nature06201
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 decade1. The importance of FPTs originates from the crucial role played by first encounter properties in various real situations, including transport in disordered media, neuron firing dynamics, 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 media1. Here we propose a general theory which allows one to accurately evaluate the mean FPT (MFPT) in complex media. Remarkably, 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 a broad range of stochastic processes characterized by length scale invariant properties. Our theoretical predictions are confirmed by numerical simulations for several emblematic models of disordered media, fractals, anomalous diffusion and scale free networks.
Benichou Olivier
Condamin Sylvain
Klafter Joseph
Tejedor Vincent
Voituriez Raphael
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