##### Department of Mathematics,

University of California San Diego

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### Math 288 - Probability & Statistics

## Morris Ang

#### UC San Diego

## Proof of the Delfino-Viti conjecture for percolation

##### Abstract:

For critical percolation on the 2D 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 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. Our arguments depend on the coupling between Liouville quantum gravity and the conformal loop ensemble.

Based on joint work with Gefei Cai, Xin Sun, and Baojun Wu.

### October 3, 2024

### 11:00 AM

AP&M 6402

Research Areas

Probability Theory****************************