Date:	Tue, October 7, 2014
Time:	9:45
Place:	Research I Seminar Room

Abstract: In this first in a series of talks on random matrix theory this semester, we will prove one of the classical, core results in this area: the Wigner semi-circular law.

Wigner matrices are Hermitian matrices generated by two families of independent and identically distributed random variables on/off the diagonal. The semi-circular law asserts that the empirical spectral distribution of this type of matrices will converge in probability to the Wigner semi-circular distribution if the matrix size tends to infinity.

The two popular proofs of this theorem are based on the moment method and the Stieltjes transform method. In Part 1 of the talk we will give a complete proof of this theorem using the moment method. Preliminary facts will be reviewed, major technical steps will be covered or sketched.