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Lecture 1: Local universality for random matrices and zeroes of random polynomials | Einstein Institute of Mathematics

Lecture 1: Local universality for random matrices and zeroes of random polynomials

Date: 
Wed, 18/03/201514:00
Location: 
Lecture Hall 2
Lecturer: 
Prof. Terence Tao, UCLA

The eigenvalues of random matrices, as well as the zeroes of random polynomials, often obey remarkable universality properties: the asymptotic distribution of these point processes (after suitable normalisation) is often independent of the distribution of the component random variables comprising the matrices or polynomials. In particular, the asymptotics of discrete random matrix or polynomial models often agree with those of their continuous counterparts.
There are now several techniques to rigorously establish this universality.
Here we focus on one such technique, based on the classical Lindeberg exchange strategy, first used to give a non-Fourier-analytic proof of the central limit theorem, and survey some of the results obtained by this method.

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