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Explore the mathematical concept of capacity in high-dimensional percolation through this 51-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 how Zhu's recent definition of branching capacity serves as an analogue in branching random walk contexts. Examine joint research introducing a capacity notion for critical bond percolation in high dimensions and understand how it shares similar properties with branching random walks. Gain insights into advanced mathematical concepts connecting potential theory, percolation theory, and random walk processes through detailed mathematical exposition and analysis.
