MIT Probability Seminar

Building 2, 147

Speaker: Jinwoo Sung (University of Chicago)Title: Supercritical LQG conditioned to be finiteAbstract:Liouville quantum gravity (LQG) in the subcritical and critical phases, corresponding to 𝛾 ≤ 2 or central charge c ≤ 1, has been extensively studied as a theory of random metric measure space and conformal field theory. On the other hand, few rigorous results about LQG with parameters outside these ranges are known, mainly for the supercritical LQG metric constructed by Ding and Gwynne. In this talk, I will discuss other properties of supercritical LQG that can be investigated from its branching structure, which is due to the coupling of supercritical LQG disk with nested CLE4 by Ang and Gwynne. There are two main results: (1) the supercritical LQG area measure, which we define as a random Borel measure locally determined by a GFF and satisfying the LQG coordinate change rule, does not exist, and (2) a natural discretization of the CLE-decorated supercritical LQG disk has the continuum random tree as its scaling limit if we condition it to have a finite number of vertices. The latter behavior was predicted by Gwynne, Holden, Pfeffer, and Remy in a pioneering paper on supercritical LQG. This is joint work with Manan Bhatia and Ewain Gwynne.