Percolation on planar graphs and applications

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Event details

Date 28.05.2025
Hour 16:0017:30
Speaker Alexander Glazman
Location
Math seminar room
Category Conferences - Seminars
Event Language English

We witness many phase transitions in everyday life (eg. ice melting to water). The mathematical approach to these phenomena revolves around the percolation model: given a graph, call each vertex open with probability p independently of the others and look at the subgraph induced by open vertices. Benjamini and Schramm conjectured in 1996 that, at p=1/2, on any planar graph, either there is no infinite connected components or infinitely many.

We prove a stronger version of this conjecture and use this to establish fractal macroscopic behaviour in the loop O(n) model. The latter includes a random discrete Lipschitz surface as a particular case.

Joint work with Matan Harel and Nathan Zelesko.

Practical information

  • Expert
  • Free

Organizer

  • Juhan Aru

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