Perfect Matchings as IID Factors on Non-Amenable Groups (2009)
Lyons, Russell, Nazarov, Fedor
We prove that in every bipartite Cayley graph of every non-amenable group, there is a perfect matching that is obtained as a factor of independent uniform random variables. We also discuss expansion...
Convolutions of Cantor measures without resonance (2009)
Nazarov, Fedor, Peres, Yuval, Shmerkin, Pablo
Denote by $\mu_a$ the distribution of the random sum $(1-a) \sum_{j=0}^\infty \omega_j a^j$, where $P(\omega_j=0)=P(\omega_j=1)=1/2$ and all the choices are independent. For $0
On the number of nodal domains of random spherical harmonics (2009)
American Journal of Mathematics - Volume 131, Number 5, October 2009
A variation on a theme of Caffarelli and Vasseur (2009)
Kiselev, Alexander, Nazarov, Fedor
Recently, using DiGiorgi-type techniques, Caffarelli and Vasseur showed that a certain class of weak solutions to the drift diffusion equation with initial data in $L^2$ gain H\"older continuity...
Global Regularity for the Critical Dispersive Dissipative Surface Quasi-Geostrophic Equation (2009)
Kiselev, Alexander, Nazarov, Fedor
We consider surface quasi-geostrophic equation with dispersive forcing and critical dissipation. We prove global existence of smooth solutions given sufficiently smooth initial data. This is done...
Convolutions of Cantor measures without resonance (2009)
Nazarov, Fedor, Peres, Yuval, Shmerkin, Pablo
Denote by $\mu_a$ the distribution of the random sum $(1-a) \sum_{j=0}^\infty \omega_j a^j$, where $P(\omega_j=0)=P(\omega_j=1)=1/2$ and all the choices are independent. For $0
A remark on the Mahler conjecture: local minimality of the unit cube (2009)
Nazarov, Fedor, Petrov, Fedor, Ryabogin, Dmitry, Zvavitch, Artem
We prove that the unit cube $B^n_{\infty}$ is a strict local minimizer for the Mahler volume product $vol_n(K)vol_n(K^*)$ in the class of origin symmetric convex bodies endowed with the Banach-Mazur...
Radial Fourier multipliers in high dimensions, preprint (2009)
Abstract. Given a fixed p � = 2 we prove a simple and effective characterization of all radial multipliers of FL p (R d) provided that the dimension d is sufficiently large. The method also yields...
Radial Fourier multipliers in high dimensions (2009)
Heo, Yaryong, Nazarov, Fedor, Seeger, Andreas
Given a fixed $p\neq 2$, we prove a simple and effective characterization of all radial multipliers of $\cF L^p(\Bbb R^d)$, provided that the dimension $d$ is sufficiently large. The method also...
New coins from old, smoothly (2008)
Holtz, Olga, Nazarov, Fedor, Peres, Yuval
Given a (known) function $f:[0,1] \to (0,1)$, we consider the problem of simulating a coin with probability of heads $f(p)$ by tossing a coin with unknown heads probability $p$, as well as a fair...
New estimates for the length of the Erdos-Herzog-Piranian lemniscate (2008)
Fryntov, Alexander, Nazarov, Fedor
Let p(z) be a monic polynomial of degree n. Consider the lemniscate L={z:|p(z)|=1}. It has been conjectured that L has the largest length when p(z)=z^n-1. We show that the length of L attains a local...
Blow up and regularity for fractal Burgers equation (2008)
Kiselev, Alexander, Nazarov, Fedor, Shterenberg, Roman
The paper is a comprehensive study of the existence, uniqueness, blow up and regularity properties of solutions of the Burgers equation with fractional dissipation. We prove existence of the finite...
The power law for the Buffon needle probability of the four-corner Cantor set (2008)
Nazarov, Fedor, Peres, Yuval, Volberg, Alexander
Let $C_n$ be the $n$-th generation in the construction of the middle-half Cantor set. The Cartesian square $K_n$ of $C_n$ consists of $4^n$ squares of side-length $4^{-n}$. The chance that a long...
On the Number of Nodal Domains of Random Spherical Harmonics (2007)
Nazarov, Fedor, Sodin, Mikhail
Let N(f) be a number of nodal domains of a random Gaussian spherical harmonic f of degree n. We prove that as n grows to infinity, the mean of N(f)/n^2 tends to a positive constant, and that N(f)/n^2...
Two weight inequalities for individual Haar multipliers and other well localized operators (2007)
Nazarov, Fedor, Treil, Sergei, Volberg, Alexander
In this paper we are proving that Sawyer type condition for boundedness work for the two weight estimates of individual Haar multipliers, as well as for the Haar shift and other "well localized"...
Transportation to random zeroes by the gradient flow (2005)
Nazarov, Fedor, Sodin, Mikhail, Volberg, Alexander
We consider the zeroes of a random Gaussian Entire Function f and show that their basins under the gradient flow of the random potential U partition the complex plane into domains of equal area. We...
Sign and area in nodal geometry of Laplace eigenfunctions (2005)
Nazarov, Fedor., Sodin, Mikhail.
American Journal of Mathematics - Volume 127, Number 4, August 2005
Coarse equidistribution of the argument of entire functions of finite order (2004)
Nazarov, Fedor, Sodin, Mikhail
We present several results that show somewhat surprising equidistribution patterns in the asymptotic behaviour of the argument of entire functions of finite order.
Sign and area in nodal geometry of Laplace eigenfunctions (2004)
Nazarov, Fedor, Polterovich, Leonid, Sodin, Mikhail
The paper deals with asymptotic nodal geometry for the Laplace-Beltrami operator on closed surfaces. Given an eigenfunction f corresponding to a large eigenvalue, we study local asymmetry of the...
Lower bounds for quasianalytic functions, II. The Bernstein quasianalytic functions (2003)
Borichev, Alexander, Nazarov, Fedor, Sodin, Mikhail
Let F be a class of functions with the uniqueness property: if a function f in F vanishes on a set of positive measure, then f is the zero function. In many instances, we would like to have a...
Nazarov, Fedor, Treil, Sergei, Volberg, Alexander
In the paper we consider Calder\'{o}n-Zygmund operators in nonhomogeneous spaces. We are going to prove the analogs of classical results for homogeneous spaces. Namely, we prove that a...
Bellman functions and two weight inequalities for Haar multipliers (1997)
Nazarov, Fedor, Treil, Sergei, Volberg, Alexander
We give necessary and sufficient conditions for two weight norm inequalities for Haar multipliers operators and for square functions. We also give sufficient conditions for two weight norm...