Probability Seminar

Random surfaces and scaling limits of 2D lattice models that are nowadays studied via LQG and SLE in probability, have been studied via  another approach called conformal field theory (CFT) since the 1980s in theoretical physics. There are three CFTs that are most relevant to 2D random geometry: Liouville CFT, minimal model and ghost CFT.  Their relevance as suggested by physics are as follows. Liouville CFT described the conformal factor of canonical random surfaces in LQG with a fixed conformal structure. The scaling limit of 2D lattice models which are nowadays studied by SLE were originally studied by minimal model CFTs. The law of the conformal structure for Brownian maps on non-simply connected surfaces, as a measure on the moduli space, is described by the ghost CFT in bosonic string theory.  I will try to clarify these pictures and give an overview of recent results and ongoing projects towards understanding them in probability. Based on joint works with Ang, Holden, Remy, Wu, Xu, Yu, Zhuang.