Séminaire de Probabilités commun ICJ/UMPA

About the elephant random walk

par Lucile Laulin

Europe/Paris
435 (UMPA)

435

UMPA

Description

The elephant random walk (ERW) is a fascinating discrete-time random walk on integers which was introduced in the early 2000s by two physicists in order to investigate how long-range memory affects the behavior of the random walk. In this talk, we will present how martingale theory or Polya-type urns can be used to obtain results on the asymptotic behavior of the ERW and its generalization to higher dimension. We will also explain how the introduction of two martingales with different speeds of convergence makes it possible to study processes related to the ERW such as the center of mass or the reinforced version.