Abstract:
It is believed that the large-scale geometric properties of 2D critical percolation are described by a logarithmic conformal field theory, but it has been challenging to exhibit concrete examples of logarithmic singularities and to find an explanation and a physical interpretation, in terms of lattice observables, for their appearance. We show that certain percolation correlation functions receive independent contributions from a large number of similar connectivity events happening at different scales. Combined with scale invariance, this leads to logarithmic divergences. Our results provide support for the validity of a CFT description of critical percolation and a step in the direction of a mathematically rigorous formulation of a logarithmic CFT of 2D critical percolation. This talk is based on joint works with Federico Camia.
Biography:
Yu Feng is currently a fifth-year Ph.D. student at Tsinghua University, advised by Prof. Hao Wu. He received his bachelor's degree from Xidian University in 2020. His research interests lie primarily in the field of probability theory, including Schramm–Loewner evolution (SLE) and statistical physics models such as percolation, random-cluster models, and the Ising model.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai
This event is open to the NYU Shanghai community and Math community.