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Gaussian Approximation of the Distribution of Strongly Repelling Particles on the Unit Circle

Student-Run Applied & Math Seminar

Speaker: Yuanyuan Xu, UC Davis
Location: 2112 MSB
Start time: Thu, Nov 30 2017, 12:10PM

Random Matrix Theory is a fast developing area with deep connections to Probability, Statistical Mechanics, Number Theory, and Quantum Theory, etc. In this talk, I will start with several important random matrix ensembles, including Wigner Matrices and beta ensembles. Then I will present some previous work on Circular beta ensemble, in particular the Circular Unitary Ensemble(CUE) and its connection to Riemann zeta function. Finally, I will set up an interacting particle system on the unit circle with stronger repulsion than that of CUE and prove the Gaussian approximation of the distribution of the particles in this model. This is joint work with Professor Soshnikov.

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