Amine Asselah: Internal DLA for Branching Random Walks скачать в хорошем качестве

Amine Asselah: Internal DLA for Branching Random Walks

Internal Dilusion Limited Aggregation is an interacting particle system that describes the growth of a random cluster governed by the boundary harmonic measure seen from an internal point. We propose a new variant of internal DLA driven by critical branching random walks. We prove that, unlike classical internal DLA, this process exhibits a phase transition in the dimension. More precisely, we establish the existence of a spherical shape theorem in dimension d ≥ 3 and the absence of a spherical shape theorem for d ≤ 2. The outer bound requires a new method to deal with the branching feature of our di!usions. Our bounds on the inner and outer worst deviations are of polynomial nature, which we expect to be a feature of this model. Recording during the thematic meeting : «Random walks: applications and interactions» the January 20, 2026 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker : Luca Récanzone Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, bibliographies, Mathematics Subject Classification - Multi-criteria search by author, title, tags, mathematical area