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Explore a mathematical lecture on Internal Diffusion Limited Aggregation (DLA) for branching random walks, presented by Amine Asselah at the Centre International de Rencontres Mathématiques. Discover a new variant of internal DLA driven by critical branching random walks, which describes the growth of random clusters governed by boundary harmonic measure from an internal point. Learn about the key finding that this process exhibits a phase transition in dimension, unlike classical internal DLA. Examine the proof establishing a spherical shape theorem's existence in dimension d ≥ 3 and its absence for d ≤ 2. Understand the new methods developed to handle the branching feature of these diffusions, particularly for outer bound calculations. Analyze the polynomial nature of bounds on inner and outer worst deviations, which represents an expected characteristic of this mathematical model. This 54-minute presentation was recorded during the thematic meeting "Random walks: applications and interactions" in January 2026, offering insights into advanced probability theory and mathematical physics applications.
