Ημερομηνία: Δευτέρα 8 Απριλίου 2019

Ώρα: 15:10 Αίθουσα: Γ31

Ομιλητής: Jason Miller, University of Cambridge

Τίτλος: Percolation in Conformal Loop Ensembles

Περίληψη:

Conformal loop ensembles (CLE) are random collections of loops in a simply connected domain, whose laws are characterized by a natural conformal invariance property. The set of points not surrounded by any CLE loop is a natural random and conformally invariant analog of the Sierpinski gasket or carpet.  Their importance is that they arise (or are conjectured to arise) as the scaling limits of all of the interfaces in a number of different planar lattice models.  We will discuss a continuum analog of the Edwards-Sokal coupling (between the q-state Potts model and the associated FK random cluster model) and its generalization to non-integer q for CLE and explain how this leads to the first description of continuous percolation interfaces in fractal domains.

Based on joint work with Scott Sheffield and Wendelin Werner.