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Seminar
FIELD Math:Analysis
DATE September 29 (Wed), 2021
TIME 14:30-15:30
PLACE Online
SPEAKER Lee , Ji Oon
HOST Kang, Nam-Gyu
INSTITUTE KAIST
TITLE Local law and Tracy-Widom limit for sparse random matrices 1
ABSTRACT

For many random matrix models, one of the fundamental inputs in the proof of universality results is the local law, which is an estimate of the local eigenvalue density. In this series of seminars, I will introduce the method based on recursive moment estimates and cumulant expansions. I will also explain how the local law and the Tracy-Widom limit for the largest eigenvalue can be proved, where the main example is a sparse random matrix.

In this talk, I will introduce the proof of the Tracy-Widom limit for Wigner matrices and explain the difference between Wigner matrices and sparse random matrices. The focus will be on the local law and several other important ingredients of the proof of the Tracy-Widom limit, such as the square-root decay at the edge and an upper bound on the largest eigenvalue.

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