Equidistribution of zeros of Random orthogonal polynomials
Dr. Koushik Ramachandran
Oklahoma State University, USA
| Speaker |
Dr. Koushik Ramachandran
Oklahoma State University, USA
|
|---|---|
| When |
Mar 08, 2018
from 04:00 PM to 05:00 PM |
| Where | LH 006 |
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Abstract: We study the asymptotic distribution of zeros for the random polynomials \(Pn(z)\) = \(\sum^n_{k=0}\xi_kB_k(z),\) where \(\{\xi_k\}^\infty_{k=0}\) are non-trivial i.i.d. complex random variables. Polynomials \(\{B_k\}^\infty_{k=0}\) are deterministic, and are selected from a standard basis such as Bergman or Szeg˝o polynomials associated with a Jordan domain G bounded by an analytic curve. We show that the zero counting measures of \(P_n\) converge almost surely to the equilibrium measure on the boundary of G if and only if \(E[log^+|\xi_0|] < \infty\). This talk is based on joint work with Igor Pritsker.