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Updated: Sep 18, 2025

Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions
Published on: February 22, 2018
Visitation Dynamics of d-Dimensional Fractional Brownian Motion
Léo Régnier1, Maxim Dolgushev1, Olivier Bénichou1
1CNRS/Sorbonne University, Laboratoire de Physique Théorique de la Matière Condensée, 4 Place Jussieu, 75005 Paris, France.
None:
The fractional Brownian motion (fBm) is a paradigmatic strongly non-Markovian process with broad applications in various fields. Despite their importance, the properties of the territory covered by a d-dimensional fBm have remained elusive so far. Here, we study the visitation dynamics of the fBm by considering the time τ_{n} required to visit a site, defined as a unit cell of a d-dimensional lattice, when n sites have been visited. Relying on scaling arguments, we determine all temporal regimes of the probability distribution function of τ_{n}. These results are confirmed by extensive numerical simulations that employ large deviation Monte Carlo algorithms. Besides these theoretical aspects, our results account for the tracking data of telomeres in the nucleus of mammalian cells, microspheres in an agorose gel, and vacuoles in the amoeba, which are experimental realizations of fBm.
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