# Student Probability Seminar

#### Universality of the Large Deviations for the Roots of Random Polynomials

Speaker: Raphael Butez

Location: Warren Weaver Hall

Date: Thursday, November 17, 2016, 2 p.m.

Synopsis:

In this talk we will study the behavior of the complex roots of random polynomials $$P= a_0 = a_1 X+...+a_n X^n$$ where the coefficients are i.i.d. random variables. We will see that when the coefficients are Gaussian random variables, the roots of $$P$$ behave like a Coulomb gas (like electrons in a conductor). We will show how we can obtain global results on the zeros of $$P$$ when the degree grows at infinity and we will answer partially to the question: how much do these results depend on the distribution of the coefficients?