Mathematics Colloquia and Seminars
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Universality and Scaling for Zeros of Random PolynomialsColloquium
|Speaker: ||Pavel Bleher, Indiana University-Purdue University Indianapolis & MSRI|
|Location: ||693 Kerr|
|Start time: ||Mon, May 24 1999, 4:10PM|
A random polynomial is a polynomial whose coefficients are
(independent) random variables, which can be real or complex. The
basic questions about real random polynomials are:
Remarkably, in the limit when N goes to infinity the joint distribution
of zeros approaches, after an appropriate rescaling, some universal
limit, which is characterized by repulsion between zeros at small
distances and fast decay of correlations at large distances. We will
discuss all these questions in the talk along with their natural
extension to zeros of complex random polynomials and to random
- How many zeros are real?
- What is the probability distribution of real zeros?
- What is the probability distribution of complex zeros?
- What are the correlations between zeros? etc., asymptotically as the degree N of the random polynomial goes to infinity.
Coffee and Tea before the talks at
3:30 in the Fifth Floor Commons Room, Kerr Hall.