A. Barbier-Chebbah

Abstract Self-interacting random walks are endowed with long-range memory effects that emerge from the interaction of the random walker at time t with the territory that it has visited at earlier times t′<t. This class of non-Markovian random walks has applications in a broad range of examples, from insects to living cells, where a random walker locally modifies its environment—leaving behind footprints along its path and, in turn, responding to its own footprints.

Abstract The statistics of first-passage times of random walks to target sites has proved to play a key role in determining the kinetics of space exploration in various contexts. In parallel, the number of distinct sites visited by a random walker and related observables has been introduced to characterize the geometry of space exploration.