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DTSTAMP:20260424T143451Z
UID:695ba6f40eae1982610021@ist.ac.at
DTSTART:20260112T170000
DTEND:20260112T180000
DESCRIPTION:Speaker: Yizheng Yuan\nhosted by Laszlo Erdös & Jan Maas\nAbst
 ract: Intrinsic metrics (a.k.a. chemical distance) and random walks on per
 colation models have been attracting a lot of mathematical attention. The 
 case of (low-dimensional) critical percolation\, however\, has remained po
 orly understood. Despite the significant progress in understanding the lar
 ge-scale geometry and scaling limits of 2D critical percolation (thanks to
  the works of Schramm\, Smirnov\, and others)\, the metric properties are 
 not captured by these results.In this talk\, I will explain how to constru
 ct the scaling limits of the intrinsic metric and the random walk on 2D cr
 itical percolation clusters. The scaling limit of the clusters as sets bel
 ongs to a class of random fractals called the conformal loop ensemble (CLE
 ) gaskets. In our work\, we construct for each CLE_\\kappa\, \\kappa \\in 
 ]4\,8[\, the canonical shortest-path metric and the canonical Brownian mot
 ion on its gasket. We show that there exists a geodesic metric (resp. diff
 usion process) on the CLE gasket that is uniquely determined by its local 
 geometry. For \\kappa=6\, we show that it is the scaling limit of the che
 mical distance metric (resp. the random walk) on critical percolation. (Fo
 r the other values of \\kappa\, they are the conjectural scaling limits of
  FK and loop O(n) models.)This talk is based on joint works with Valeria A
 mbrosio\, Irina ankovi\, Maarten Markering\, and Jason Miller. 
LOCATION:Central Bldg / O1 / Mondi 2a (I01.O1.008)\, ISTA
ORGANIZER:boosthui@ist.ac.at
SUMMARY:Yizheng Yuan: The intrinsic metric and the random walk on 2D critic
 al percolation and CLE
URL:https://talks-calendar.ista.ac.at/events/6226
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