Related Experiment Video
Updated: May 31, 2026

The Diffusion of Passive Tracers in Laminar Shear Flow
Published on: May 1, 2018
Universality classes of first-passage-time distribution in confined media
B Meyer1, C Chevalier, R Voituriez
1Laboratoire de Physique Théorique de la matière Condensée (UMR 7600), Université Paris 6, Paris, France.
Abstract:
We study the first-passage time (FPT) distribution to a target site for a random walker evolving in a bounded domain. We show that in the limit of large volume of the confining domain, this distribution falls into universality classes indexed by the walk dimension d(w) and the fractal dimension d(f) of the medium, which have been recently identified previously [Bénichou et al., Nat. Chem. 2, 472 (2010)]. We present in this paper a complete derivation of these universal distributions, discuss extensively the range of applicability of the results, and extend the method to continuous-time random walks. This analysis puts forward the importance of the geometry, and in particular the position of the starting point, in first-passage statistics. Analytical results are validated by numerical simulations, applied to various models of transport in disordered media, which illustrate the universality classes of the FPT distribution.
Related Concept Videos
Probability Distributions
A discrete probability distribution is a probability distribution of discrete random variables. It can be categorized into binomial probability distribution and Poisson probability...
Poisson Probability Distribution
The...
First Law: Particles in One-dimensional Equilibrium
The Integrated Rate Law: The Dependence of Concentration on Time
Uniform Distribution
Noncompartmental Analysis: Mean Residence Time
After the administration of a drug through intravenous bolus injection, the drug molecules are distributed throughout the body and remain there for varying periods. The MRT represents the average time these drug molecules stay in the...

