Martin boundary for random walks in cones

par Pierre Tarrago

jeudi 30 nov. 2023, 14:00 → 15:00 Europe/Paris

In this talk, I will explain the role played by positive harmonic functions when conditioning a random walk to remain in a domain, and how Martin boundary theory allows to qualitatively describe those functions. Then, I will present recent results on the description of the Martin boundary in the special case where the domain is a convex cone (joint work with Jetlir Duraj, Viet Hung Hoang, Kilian Raschel and Vitali Wachtel). If time permits, I will briefly introduce the notion of space-time Martin boundary, a refinement of the usual Martin boundary that allows a finer conditioning of the random walk.