External seminar - Léo Régnier (LPENS)

Abstract: How long does it take for a tracer to reach a position it has never visited before [1]? When will a forager starve to death, depending on the medium it moves through or its walking behavior [2]?  In this presentation, I will address these two questions by quantifying the exploration dynamics of a memoryless (Markovian) random walk using the time between visits to new sites. We will observe that this observable displays universal behaviors. Next, we will see how these findings apply to the foraging random walk problem, where the tracer has a finite metabolic time, serving as a minimal model for a depletion-controlled system.

References:
[1] Régnier, L., Dolgushev, M., Redner, S. & Bénichou, O., Universal exploration dynamics of random walks. Nat Commun 14, 618 (2023)
[2] Régnier, L., Dolgushev, M. & Bénichou, O., From Maximum of Inter-Visit Times to Starving Random Walks, Phys. Rev. Lett. 132, 127101 or  Arxiv (2023)