2023.12.1 16:00 N613

In the 2D critical Bernoulli percolation, the n-point connectivity $P_n(x_1,…,x_n)$ is defined to be the probability that $x_1,…,x_n$ are in the same cluster. Delfino-Viti'10 conjectures that the ratio $R=P_3(x_1,x_2,x_3)/\sqrt{P_2(x_1,x_2)P_2(x_1,x_3)P_2(x_2,x_3)}$ will converge to a universal constant, independent of $x_1,x_2,x_3$, which can be expressed through the imaginary DOZZ formula. This formula gives R≈1.022 and matches the numerical simulation. In this talk we rigorously prove Delfino-Viti conjecture, from the coupling results of Liouville quantum gravity and conformal loop ensemble developed recently. Our approach also solves 3-point connectivities of 2D critical FK-q percolations and 3-point connectivity of spin clusters in 2D critical Ising model.

This talk is based on the joint work with Morris Ang (Columbia), Xin Sun(BICMR) and Baojun Wu(BICMR).