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Two-Dimensional Random Geometry
Proof of the Delfino-Viti conjecture
Morris Ang, UC San Diego
Monday, July 8, 2024
Abstract: For critical percolation on the triangular lattice, consider the probability that three points lie in the same cluster. The Delfino-Viti conjecture predicts that in the fine mesh limit, under suitable normalization, this probability converges to (a multiple of) the imaginary DOZZ formula from conformal field theory. We prove the Delfino-Viti conjecture, and more generally, obtain the cluster connectivity three-point function of the conformal loop ensemble. Based on joint work with Gefei Cai, Xin Sun, and Baojun Wu.