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Article Dans Une Revue Nature Communications Année : 2023

Universal exploration dynamics of random walks

Résumé

The territory explored by a random walk is a key property that may be quantified by the number of distinct sites that the random walk visits up to a given time. We introduce a more fundamental quantity, the time τ n required by a random walk to find a site that it never visited previously when the walk has already visited n distinct sites, which encompasses the full dynamics about the visitation statistics. To study it, we develop a theoretical approach that relies on a mapping with a trapping problem, in which the spatial distribution of traps is continuously updated by the random walk itself. Despite the geometrical complexity of the territory explored by a random walk, the distribution of the τ n can be accounted for by simple analytical expressions. Processes as varied as regular diffusion, anomalous diffusion, and diffusion in disordered media and fractals, fall into the same universality classes.
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Dates et versions

hal-03979436 , version 1 (08-02-2023)

Identifiants

Citer

Léo Régnier, Maxim Dolgushev, S. Redner, Olivier Bénichou. Universal exploration dynamics of random walks. Nature Communications, 2023, 14 (1), pp.618. ⟨10.1038/s41467-023-36233-5⟩. ⟨hal-03979436⟩
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