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SUMMARY:Metrics and random walks on 2D critical percolation and CLE - Yizh
 eng Yuan
DTSTART:20250513T130000Z
DTEND:20250513T140000Z
UID:TALK231955@talks.cam.ac.uk
CONTACT:Jason Miller
DESCRIPTION:Intrinsic metrics (a.k.a. chemical distance) and random walks 
 on percolation models have been attracting a lot of mathematical attention
 . The case of (low-dimensional) critical percolation\, however\, has remai
 ned poorly understood. In this talk\, I will explain how to construct the 
 scaling limits of the intrinsic metric and the random walk on 2D critical 
 percolation clusters. More generally\, for each CLE_\\kappa\, \\kappa \\in
  ]4\,8[\, we construct the canonical shortest-path metric and diffusion pr
 ocess on its gasket. We show that the metrics are uniquely characterised b
 y their Markovian property\, and that they are scale-covariant and conform
 ally covariant.\n\nThis talk is based on joint works with Valeria Ambrosio
 \, Irina Đanković\, Maarten Markering\, and Jason Miller.
LOCATION:MR12
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