The Minkowski Content Measure for the Liouville Quantum Gravity Metric

Probability and analysis informal seminarA Liouville quantum gravity (LQG) surface is a random two-dimensional « Riemannian manifold » that is conjectured to be the scaling limit of a wide variety of random planar graph models. LQG was formulated initially as a random measure space and, more recently, as a random metric space. In this talk, I will explain how the LQG measure can be recovered as the Minkowski content measure for the LQG metric, thereby providing a direct connection between the two formulations for the first time. Our primary tool is the mating-of-trees theory of Duplantier, Miller, and Sheffield, which says that an LQG surface explored by an independent space-filling Schramm–Loewner evolution (SLE) curve is an infinitely divisible metric measure space when. This is joint work with Ewain Gwynne (University of Chicago). ========Pour être informé des prochains séminaires vous pouvez vous abonner à la liste de diffusion en écrivant un mail à sympa@listes.math.cnrs.fr avec comme sujet: « subscribe seminaire_mathematique PRENOM NOM »(indiquez vos propres prénom et nom) et laissez le corps du message vide.