Topics in random matrix theory: the semicircle law, inverse Littlewood-Offord theory, least singular values, and the circular law III

Terence Tao
University of California, Los Angeles (UCLA)

We present three loosely related topics in random matrix theory. Firstly, we show how the moment method can be used to establish the semicircular law for the bulk distribution of random matrices of Wigner type. Then, we present some inverse Littlewood-Offord theory, and explain how it is used to bound least singular values of random matrices. Finally, these methods are combined to establish the circular law for random matrices with iid entries.

Presentation (PDF File)

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