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Talk

On the peeling process of random planar maps

  • Nicolas Curien (Université Paris-Sud Orsay, France)
A3 01 (Sophus-Lie room)

Abstract

The spatial Markov property of random planar maps is arguably one of the most useful properties of these random lattices. Roughly speaking, it says that after exploring a region of the map, the law of the remaining part only depends on the perimeter of the discovered region. It has been first heuristically used by Watabiki in the physics literature under the name of "peeling process" but was rigorously defined in 2003 by Angel in the case of the Uniform Infinite Planar Triangulation (UIPT). Since then, it has been used to derive information about the metric, (bernoulli and first passage) percolation, simple random walk and recently about the conformal structure of random planar maps. It is also at the core of the construction of "hyperbolic" random maps. In this talk, we will introduce smoothly the peeling process and present some of its main applications.

Katja Heid

MPI for Mathematics in the Sciences Contact via Mail

Upcoming Events of this Seminar

  • Tuesday, 04.06.24 tba with Vadim Gorin
  • Tuesday, 11.06.24 tba
  • Tuesday, 25.06.24 tba with Paul Dario
  • Tuesday, 25.06.24 tba with Julian Fischer
  • Tuesday, 16.07.24 tba with Michael Loss
  • Tuesday, 20.08.24 tba with Tomasz Komorowski
  • Tuesday, 03.12.24 tba with Patricia Gonçalves