Turgay Bayraktar

activity

20062026

most citedZero distribution of random sparse polynomials

34 citations · 128 across the 31 of their papers we have counts for

collaborators

32 papers

math.CV2026

Asymptotic expansion of induced Grassmannian Chern forms and distribution of random degeneracy sets

Turgay Bayraktar, Dan Coman, Bingxiao Liu +1

For the Grassmannian embeddings defined by the spaces $H^{0} (X, L^{p} \otimes E)$ , where $L$ is a positive line bundle and $E$ is a holomorphic vector bundle over a compact complex manif…

math.AG2026

On Nests and Large Components of Random Real Algebraic Curves

Ali Ulaş Özgür Kişisel, Turgay Bayraktar

We develop a variant of the barrier method in order to address questions about topology of Kostlan random real algebraic plane curves. In particular we prove that the expected numb…

math.CV2026

Zeros of random $P$ -polynomials in $C^{d}$ with exponential profiles

Turgay Bayraktar, Afrim Bojnik

We study random multivariate $P$ -polynomials in $C^{d}$ with monomial supports constrained to $n P \cap Z_{+}^{d}$ for a convex body $P \subset R_{+}^{d}$ , and determin…

math.CV2025

Tian's theorem for Grassmannian embeddings and degeneracy sets of random sections

Turgay Bayraktar, Dan Coman, Bingxiao Liu +1

Let $(X, ω)$ be a compact Kähler manifold, $(L, h^{L})$ be a positive line bundle, and $(E, h^{E})$ be a Hermitian holomorphic vector bundle of rank $r$ on $X$ . We prove that the pullback…

math.CV2025

Asymptotic Mass Distribution of Random Holomorphic Sections

Turgay Bayraktar, Afrim Bojnik

In this note, we prove a central limit theorem for the mass distribution of random holomorphic sections associated with a sequence of positive line bundles endowed with $\mathscr{C…

math.CV2025

Widom factors in $C^{n}$

Gökalp Alpan, Turgay Bayraktar, Norm Levenberg

We generalize the theory of Widom factors to the $C^{n}$ setting. We define Widom factors of compact subsets $K \subset C^{n}$ associated with multivariate orthogonal po…

math.CV2024

Zeros of random holomorphic sections of big line bundles with continuous metrics

Turgay Bayraktar, Dan Coman, George Marinescu +1

Let $X$ be a compact normal complex space, $L$ be a big holomorphic line bundle on $X$ and $h$ be a continuous Hermitian metric on $L$ . We consider the spaces of holomorphic sectio…

math.AG2023★ 2 cited

Expected Multivolumes of Random Amoebas

Turgay Bayraktar, Ali Ulaş Özgür Kişisel

We compute the expected multivolume of the amoeba of a random half dimensional complete intersection in $CP^{2 n}$ . We also give a relative generalization of our result to…

math.CV2023

Zero Distribution of Random Bernoulli Polynomial Mappings

Turgay Bayraktar, Çiğdem Çelik

In this note, we study asymptotic zero distribution of multivariable full system of random polynomials with independent Bernoulli coefficients. We prove that with overwhelming prob…

math.AG2022

An Exponential Rarefaction Result for Sub-Gaussian Real Algebraic Maximal Curves

Turgay Bayraktar, Emel Karaca

We prove that maximal real algebraic curves associated with sub-Gaussian random real holomorphic sections of a smoothly curved ample line bundle are exponentially rare. This genera…

math.CV2022★ 3 cited

On Dynamics of Asymptotically Minimal Polynomials

Turgay Bayraktar, Melike Efe

We study dynamical properties of asymptotically extremal polynomials associated with a non-polar planar compact set E. In particular, we prove that if the zeros of such polynomials…

math.CV2021★ 3 cited

Random Polynomials in Several Complex Variables

Turgay Bayraktar, Tom Bloom, Norm Levenberg

We generalize some previous results on random polynomials in several complex variables. A standard setting is to consider random polynomials $H_{n} (z) := \sum_{j = 1}^{m_{n}} a_{j} p_{j} (z)$ th…

math.AG2021

The Expected Depth of Random Real Algebraic Plane Curves

Turgay Bayraktar, Ali Ulaş Özgür Kişisel

In this note we study asymptotic isotopy of random real algebraic plane curves. More precisely, we obtain a Kac-Rice type formula that gives the expected number of two-sided compon…

math.CV2020

Fekete Points as Norming Sets for Random Holomorphic Sections

Turgay Bayraktar

We prove that Fekete configurations associated with a positive Hermitian line bundle over a compact Kähler manifold are asymptotically exact norming sets for random holomorphic sec…

math.CV2019★ 6 cited

Pluripotential Theory and Convex Bodies: A Siciak-Zaharjuta theorem

T. Bayraktar, S. Hussung, N. Levenberg +1

We work in the setting of weighted pluripotential theory arising from polynomials associated to a convex body $P$ in $(R^{+})^{d}$ . We define the {\it logarithmic indicator funct…

math.CV2018★ 3 cited

Mass equidistribution for random polynomials

Turgay Bayraktar

The purpose of this note is to study asymptotic zero distribution of multivariate random polynomials as their degrees grow. For a smooth weight function with super logarithmic grow…

math.CV2018

Pluripotential Theory and Convex Bodies: Large Deviation Principle

Turgay Bayraktar, Thomas Bloom, Norman Levenberg +1

We continue the study in a previous work in the setting of weighted pluripotential theory arising from polynomials associated to a convex body $P$ in $(R^{+})^{d}$ . Our goal is t…

math.CV2018★ 1 cited

A survey on zeros of random holomorphic sections

Turgay Bayraktar, Dan Coman, Hendrik Herrmann +1

We survey results on the distribution of zeros of random polynomials and of random holomorphic sections of line bundles, especially for large classes of probability measures on the…

math.CV2017★ 6 cited

On global universality for zeros of random polynomials

Turgay Bayraktar

In this work, we study asymptotic zero distribution of random multi-variable polynomials which are random linear combinations $\sum_{j} a_{j} P_{j} (z)$ with i.i.d coefficients relative t…

math.CV2017★ 16 cited

Universality results for zeros of random holomorphic sections

Turgay Bayraktar, Dan Coman, George Marinescu

In this work we prove an universality result regarding the equidistribution of zeros of random holomorphic sections associated to a sequence of singular Hermitian holomorphic line…

math.DS2017

Almost Sure Invariance Principle for non-autonomous holomorphic dynamics in $P^{k}$

Turgay Bayraktar

We prove almost sure invariance principle, a strong form of approximation by Brownian motion, for non-autonomous holomorphic dynamical systems on complex projective space $\Bbb{P}^…

math.CV2016★ 13 cited

Pluripotential Theory and Convex Bodies

Turgay Bayraktar, Thomas Bloom, Norman Levenberg

In their seminal paper, Berman and Boucksom exploited ideas from complex geometry to analyze asymptotics of spaces of holomorphic sections of tensor powers of certain line bundles…

math.CV2016★ 7 cited

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

Turgay Bayraktar

In this note, we obtain asymptotic expected number of real zeros for random polynomials of the form $f_{n} (z) = j = 0 \sum n a_{j}^{n} c_{j}^{n} z^{j}$ where $a_{j}^{n}$ are independent and identical…

math.CV2016★ 9 cited

Asymptotic normality of linear statistics of zeros of random polynomials

Turgay Bayraktar

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…

Asymptotic expansion of induced Grassmannian Chern forms and distribution of random degeneracy sets

On Nests and Large Components of Random Real Algebraic Curves

Zeros of random P-polynomials in Cd with exponential profiles

Tian's theorem for Grassmannian embeddings and degeneracy sets of random sections

Asymptotic Mass Distribution of Random Holomorphic Sections

Widom factors in Cn

Zeros of random holomorphic sections of big line bundles with continuous metrics

Expected Multivolumes of Random Amoebas

Zero Distribution of Random Bernoulli Polynomial Mappings

An Exponential Rarefaction Result for Sub-Gaussian Real Algebraic Maximal Curves

On Dynamics of Asymptotically Minimal Polynomials

Random Polynomials in Several Complex Variables

The Expected Depth of Random Real Algebraic Plane Curves

Fekete Points as Norming Sets for Random Holomorphic Sections

Pluripotential Theory and Convex Bodies: A Siciak-Zaharjuta theorem

Mass equidistribution for random polynomials

Pluripotential Theory and Convex Bodies: Large Deviation Principle

A survey on zeros of random holomorphic sections

On global universality for zeros of random polynomials

Universality results for zeros of random holomorphic sections

Almost Sure Invariance Principle for non-autonomous holomorphic dynamics in Pk

Pluripotential Theory and Convex Bodies

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

Asymptotic normality of linear statistics of zeros of random polynomials

Zeros of random $P$ -polynomials in $C^{d}$ with exponential profiles

Widom factors in $C^{n}$

Almost Sure Invariance Principle for non-autonomous holomorphic dynamics in $P^{k}$