Turgay Bayraktar

Zero distribution of random sparse polynomials

We study asymptotic zero distribution of random Laurent polynomials whose support are contained in dilates of a fixed integral polytope

Asymptotic normality of linear statistics of zeros of random polynomials

P

Expected number of real roots for random linear combinations of orthogonal polynomials associated with radial weights

as their degree grow. We consider a large class of probability distributions including the ones induced from i.i.d. random coefficients whose distribution law has bounded density with logarithmically decaying tails as well as moderate measures defined over the projectivized space of Laurent polynomials. We obtain a quantitative localized version of Bernstein-Kouchnirenko Theorem.

Almost sure invariance principle for non-autonomous holomorphic dynamics in ℙ^{}

In this note, we prove a central limit theorem for smooth linear statistics of zeros of random polynomials which are linear combinations of orthogonal polynomials with iid standard complex Gaussian coefficients. Along the way, we obtain Bergman kernel asymptotics for weighted

Constraints on automorphism groups of higher dimensional manifolds

L^2

Equidistribution of zeros of random holomorphic sections

-space of polynomials endowed with varying measures of the form

On the automorphism group of rational manifolds

e^{-2n\varphi_n(z)}dz

A survey on zeros of random holomorphic sections

under suitable assumptions on the weight functions

Pluripotential theory and convex bodies

\varphi_n

Universality results for zeros of random holomorphic sections

.