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Chemical distance in high-dimensional percolation

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  • UserJack Hanson (Universität Hamburg)
  • ClockTuesday 03 February 2026, 14:00-15:00
  • HouseMR12.

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Abstract: Since at least the 1970s, transport properties of critical percolation have been studied in both the physics and mathematics literature. Improving our understanding requires sharp estimates on large-scale geometric properties of critical percolation clusters, including the intrinsic (``chemical’‘) distance and electrical resistance. We show a sharp result for these in high dimensions: the distance and resistance between the origin and a distant vertex converges in distribution when rescaled by a multiple of the square of the Euclidean distance, conditional on these vertices lying in the same cluster.

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