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Explore the mathematical concept of capacity in the context of branching random walks and percolation theory in this 48-minute conference talk. Learn about the classical notion of capacity in potential theory as a measure of set size from the perspective of random walks or Brownian motion. Discover Zhu's recent definition of branching capacity as the analogue of capacity for branching random walks. Examine joint research with Amine Asselah and Bruno Schapira that introduces a capacity notion for critical bond percolation sets. Understand how this new capacity concept shares similar properties with branching random walk capacity. Gain insights into advanced probability theory and mathematical physics through this specialized presentation recorded during the thematic meeting "Interacting particle systems and related fields" at the Centre International de Rencontres Mathématiques in Marseille, France.
