O. Yakir

activity

20182026

most citedFluctuations of linear statistics for Gaussian perturbations of the lattice

Z^{d}

6 citations · 13 across the 12 of their papers we have counts for

collaborators

Showing 2020Show all

4 papers · 1 filter

math.CV2020

Approximately half of the roots of a random Littlewood polynomial are inside the disk

Oren Yakir

We prove that for large $n$ , all but $o (2^{n})$ polynomials of the form $P (z) = \sum_{k = 0}^{n - 1} \pm z^{k}$ have $n /2 + o (n)$ roots inside the unit disk. This solves a problem from Ha…

math.PR2020★ 6 cited

Fluctuations of linear statistics for Gaussian perturbations of the lattice $Z^{d}$

Oren Yakir

We study the point process $W$ in $R^{d}$ obtained by adding an independent Gaussian vector to each point in $Z^{d}$ . Our main concern is the asymptotic size of fluct…

math.PR2020

The minimum modulus of Gaussian trigonometric polynomials

Oren Yakir, Ofer Zeitouni

We prove that the minimum of the modulus of a random trigonometric polynomial with Gaussian coefficients, properly normalized, has limiting exponential distribution.

math.PR2020

Recovering the lattice from its random perturbations

Oren Yakir

Given a $d$ -dimensional Euclidean lattice we consider the random set obtained by adding an independent Gaussian vector to each of the lattice points. In this note we provide a simp…

Approximately half of the roots of a random Littlewood polynomial are inside the disk

Fluctuations of linear statistics for Gaussian perturbations of the lattice Zd

The minimum modulus of Gaussian trigonometric polynomials

Recovering the lattice from its random perturbations

Fluctuations of linear statistics for Gaussian perturbations of the lattice $Z^{d}$