Léo REGNIER & Anna RITZ ZWILLING

How long does it take for a tracer to reach a position it has never visited before [1]? And 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. Firstly, I will quantify the exploration dynamics of a memoryless (Markovian) random walk using the time between visits to new sites, which statistics can be separated in three universality classes depending on a few parameters of the walk.Next, I will apply these findings to the foraging random walk problem. Here, the tracer has a finite metabolic time, serving as a minimal model for a depletion-controlled system. In addressing this problem, we will demonstrate how to determine the lifetime, a question that remained elusive prior to this work.