Title：A quadratic BSDE approach to normalization for the finite volume 2D sine-Gordon model in the finite ultraviolet regime

Abstract：In this presentation, we discuss a new construction of the 2D sine-Gordon model on bounded domains by a novel normalization technique in the finite ultraviolet regime. Our methodology involves a family of backward stochastic differential equations (BSDEs) driven by a cylindrical Wiener process, whose generators are purely quadratic functions of the second unknown variable. The terminal conditions of the quadratic BSDEs are uniformly bounded and converge in probability to the real part of complex multiplicative chaos tested against an arbitrarily given test function, which helps us describe our sine-Gordon measure through some delicate estimates concerning bounded mean oscillation (BMO) martingales. As the ultraviolet cutoffs are vanishing, the quadratic BSDEs converge to a quadratic BSDE that completely characterizes the absolute continuity of our sine-Gordon measure with respect to the law of Gaussian free fields. Our approach can also be used effectively to establish the connection between our sine-Gordon measure and the scaling limit of correlation functions of the critical planar XOR-Ising model and to prove the weak convergence of the normalized charge distributions of 2D log-gases.

Speaker：Rundong Xv， Fudan University

Date：4:00pm-6:00pm 2025-4-14（Monday）.

Venue: Room 204, School of Mathematical Science

Inviter：Qiang Han

All faculty and students are welcome to attend!