The extremal process in nested conformal loops

Elie Aidekon


By analogy with the Liouville measures constructed by Duplantier and Sheffield in the case of the Gaussian Free Field, we construct a random measure on the unit disc related to a collection of nested conformal loops. Then, we study the extremal process associated to points in the disc with high conformal radius. We show that it gives a decorated Poisson point process, as can be expected from the analogy with branching Brownian motion.

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