First-passage times in complex scale-invariant media

Abstract

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.

Submitted version. Supplementary Informations available on Nature website

References in corpus (10)

• Emergence of scaling in random networks
• The diameter of the world wide web
• Self-similarity of complex networks
• Global organization of metabolic fluxes in the bacterium, Escherichia coli
• Origins of fractality in the growth of complex networks
• Optimal search strategies for hidden targets
• Exact first-passage exponents of 1D domain growth: relation to a reaction diffusion model
• Scaling theory of transport in complex networks
• First-passage times for random walks in bounded domains
• Bidimensional intermittent search processes: an alternative to Levy flights strategies

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