We will study the spectral properties of the random matrix of SYK model, which is a simple model of the black hole in physics literature. Our primary interest is the distribution of the eigenvalues as the number of Majorana fermions tends to infinity. We will first prove that there is a phase transition for the global density of eigenvalues, and then we show that the linear statistics of eigenvalues satisfy the central limit theorem. In the end, we study the largest eigenvalue of SYK model. This is my joint work with G. Tian and D. Wei.
Renjie Feng is an Assistant Professor at Beijing International Center for Mathematical Research, Peking University. He received Ph.D. from Northwestern University in 2012 and was a Postdoc at McGill University and University of Maryland, College Park. His research interest lies in random geometry and random matrix theory such as SYK model.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai
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