External Lecturer:
Kohei Suzuki
Course Type:
PhD Course
Academic Year:
2024-2025
Period:
May - June
Duration:
20 h
Description:
Abstract: The study of interacting particles has been a central subject in statistical physics. The goal of this course is to study interacting infinitely many Brownian motions with long range interaction by using methods from extended metric measure geometry and optimal transport theory. The lectures will cover several topics from the following subjects:
• Extended metric measure geometry of the configuration space
• Dirichlet forms associated with infinite interacting Brownian motions
• Ricci curvature lower bounds for interacting Brownian motions
• gradient flows in the space of probability measures over the configuration space
• determinantal point processes and Gibbs measures
• Application to Dyson Brownian motions
This course is suitable for anyone who has a background in differential/metric measure geometry, random matrices, stochastic differential equations or Dirichlet forms.
References:
• Albeverio, S., Kondratiev, Yu. G., and Röckner, M. Analysis and Geometry on Configuration Spaces. J. Funct. Anal., 154(2):444–500, 1998.
• Albeverio, S., Kondratiev, Yu. G., and Röckner, M. Analysis and Geometry on Configuration Spaces: The Gibbsian Case.J. Funct. Anal., 157:242–291, 1998.
• Erbar, M. and Huesmann, M. Curvature bounds for configuration spaces. Calc. Var., 54:307–430, 2015.
• Dello Schiavo, L. and Suzuki, K. Configuration Spaces over Singular Spaces II – Curvature. arXiv:2205.01379, 2022.
• Suzuki, K. Curvature Bound of Dyson Brownian Motion. arXiv:2301.00262, 2022.
Research Group: