Percolation Today is an online seminar aiming to promote the exchange of exciting new ideas on both Bernoulli and dependent percolation processes, at a level appropriate for specialists in the area. We hope to be a focal point to foster new connections and collaborations between the global community of percolation lovers.

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Next Talk

Fractal properties of the critical random cluster model on \mbox{\LARGE{\mathds{Z}^2}}

Date: Tuesday September 22, 16:15 CEST.

Speaker: Hugo Duminil-Copin

Abstract: This talk will be studying the critical regime of the planar random-cluster model on \mathds{Z}^2 with cluster-weight q\in [1,4). More precisely, we will explain how one derives crossing estimates in quads which are uniform in their boundary conditions and depend only on the extremal lengths of the quads. These estimates have important consequences concerning the sub-sequential scaling limits of the collection of interfaces between primal and dual clusters, arm-exponents, quasi-multiplicativity, etc.
This is a joint work with Ioan Manolescu and Vincent Tassion.

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Hugo Duminil-Copin
Tom Hutchcroft
Vincent Tassion

Pictures by:
 Adèle Ivain and Laurie Quétel