Logarithmic Correlation Functions in 2D Critical Percolation
报告人： 冯昱（清华大学)
时间：2025-03-03 14:00-15:00
地点：智华楼四元厅-225
Abstract:
We will explore the connection between connection probabilities in random cluster models and correlation functions in conformal field theory (CFT). The discussion is divided into two parts. In the first, we focus on the critical FK-Ising model and derive the scaling limits of a general class of boundary-to-boundary connection probabilities. Our results are consistent with predictions from the corresponding CFT. In the second part, we turn to critical percolation and demonstrate that certain percolation correlation functions receive independent contributions from a large number of connectivity events occurring at different scales. When combined with scale invariance, this leads to logarithmic divergences. Our results provide a step in the direction of a mathematically rigorous formulation of a logarithmic CFT for 2D critical percolation. Based on joint works with Federico Camia, Eveliina Peltola, and Hao Wu.
About the Speaker:
冯昱，清华大学数学系博士生，导师为吴昊教授。主要研究兴趣包括SLE与统计物理模型（渗流模型、伊辛模型等）。
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