Universal exploration dynamics of random walks.

ABSTRACT: 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 var

SUBMITTER: Regnier L 

PROVIDER: S-EPMC9899275 | biostudies-literature | 2023 Feb

REPOSITORIES: biostudies-literature