Ontology highlight
ABSTRACT:
SUBMITTER: Regnier L
PROVIDER: S-EPMC9899275 | biostudies-literature | 2023 Feb
REPOSITORIES: biostudies-literature
Régnier Léo L Dolgushev Maxim M Redner S S Bénichou Olivier O
Nature communications 20230204 1
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<sub>n</sub> 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 ...[more]