Alexandros Eskenazis

activity

20132026

most citedGaussian mixtures: entropy and geometric inequalities

52 citations · 81 across the 18 of their papers we have counts for

collaborators

28 papers

math.MG2026

The dimension-free threshold for maximal sections of $ℓ_{p}$

Silouanos Brazitikos, Alexandros Eskenazis

We prove the existence of a sharp threshold $p_{0} \approx 26.265 \dots$ , such that for every $n \in N$ and $p \geq p_{0}$ , the volume maximizing section of the unit ball of $\el…

math.MG2026

Functional perimeter and the dimensional Brunn-Minkowski inequality for log-concave measures

Alexandros Eskenazis, Apostolos Giannopoulos, Natalia Tziotziou

This paper is dedicated to two geometric problems associated to log-concave measures on $R^{n}$ . First, we study the dimensional Brunn-Minkowski inequality for even log-conc…

cs.DS2025

An optimal algorithm for average distance in typical regular graphs

Alexandros Eskenazis, Manor Mendel, Assaf Naor

We design a deterministic algorithm that, given $n$ points in a \emph{typical} constant degree regular~graph, queries $O (n)$ distances to output a constant factor approximation to…

math.FA2025

Concavity principles for weighted marginals

Dario Cordero-Erausquin, Alexandros Eskenazis

We develop a general framework to study concavity properties of weighted marginals of $β$ -concave functions on $R^{n}$ via local methods. As a concrete implementation of our…

math.CA2023

Approximation of polynomials from Walsh tail spaces

Alexandros Eskenazis, Haonan Zhang

We derive various bounds for the $L_{p}$ distance of polynomials on the hypercube from Walsh tail spaces, extending some of Oleszkiewicz's results (2017) for Rademacher sums.

math.MG2023

Some geometric applications of the discrete heat flow

Alexandros Eskenazis

We present two geometric applications of heat flow methods on the discrete hypercube ${- 1, 1}^{n}$ . First, we prove that if $X$ is a finite-dimensional normed space, then the bi-Lip…

cs.IT2023

On the entropy and information of Gaussian mixtures

Alexandros Eskenazis, Lampros Gavalakis

We establish several convexity properties for the entropy and Fisher information of mixtures of centered Gaussian distributions. First, we prove that if $X_{1}, X_{2}$ are independent…

math.FA2023★ 2 cited

Discrete logarithmic Sobolev inequalities in Banach spaces

Dario Cordero-Erausquin, Alexandros Eskenazis

Let $C_{n} = {- 1, 1}^{n}$ be the discrete hypercube equipped with the uniform probability measure $σ_{n}$ . We prove that if $(E, ∥ \cdot ∥_{E})$ is a Banach space of finite cotype…

math.PR2023

Intrinsic dimensional functional inequalities on model spaces

Alexandros Eskenazis, Yair Shenfeld

We initiate a systematic study of intrinsic dimensional versions of classical functional inequalities which capture refined properties of the underlying objects. We focus on model…

math.PR2023★ 3 cited

Distributional stability of the Szarek and Ball inequalities

Alexandros Eskenazis, Piotr Nayar, Tomasz Tkocz

We prove an extension of Szarek's optimal Khinchin inequality (1976) for distributions close to the Rademacher one, when all the weights are uniformly bounded by a $1/ 2$ fract…

math.FA2022★ 3 cited

Resilience of cube slicing in $ℓ_{p}$

Alexandros Eskenazis, Piotr Nayar, Tomasz Tkocz

Ball's celebrated cube slicing (1986) asserts that among hyperplane sections of the cube in $R^{n}$ , the central section orthogonal to $(1, 1, 0, \dots, 0)$ has the greatest vol…

cs.LG2022

Low-degree learning and the metric entropy of polynomials

Alexandros Eskenazis, Paata Ivanisvili, Lauritz Streck

Let $F_{n, d}$ be the class of all functions $f : {- 1, 1}^{n} \to [- 1, 1]$ on the $n$ -dimensional discrete hypercube of degree at most $d$ . In the first part of this paper, we p…

math.PR2022★ 3 cited

Sharp Rosenthal-type inequalities for mixtures and log-concave variables

Giorgos Chasapis, Alexandros Eskenazis, Tomasz Tkocz

We obtain Rosenthal-type inequalities with sharp constants for moments of sums of independent random variables which are mixtures of a fixed distribution. We also identify extremis…

math.MG2022

Average distortion embeddings, nonlinear spectral gaps, and a metric John theorem (after Assaf Naor)

Alexandros Eskenazis

We survey various aspects of the theory of nonlinear spectral gaps. In particular, we present a self-contained proof of Naor's average John theorem.

cs.LG2021

Learning low-degree functions from a logarithmic number of random queries

Alexandros Eskenazis, Paata Ivanisvili

We prove that every bounded function $f : {- 1, 1}^{n} \to [- 1, 1]$ of degree at most $d$ can be learned with $L_{2}$ -accuracy $ε$ and confidence $1 - δ$ from $\log(\tfrac{n}δ)\,\va…

math.CA2020

Sharp growth of the Ornstein-Uhlenbeck operator on Gaussian tail spaces

Alexandros Eskenazis, Paata Ivanisvili

Let $X$ be a standard Gaussian random variable. For any $p \in (1, \infty)$ , we prove the existence of a universal constant $C_{p} > 0$ such that the inequality $$(\mathbb{E} |h'(X)|…

math.FA2020

Talagrand's influence inequality revisited

Dario Cordero-Erausquin, Alexandros Eskenazis

Let $C_{n} = {- 1, 1}^{n}$ be the discrete hypercube equipped with the uniform probability measure $σ_{n}$ . Talagrand's influence inequality (1994) asserts that there exists $C\i…

math.MG2020

The dimensional Brunn-Minkowski inequality in Gauss space

Alexandros Eskenazis, Georgios Moschidis

Let $γ_{n}$ be the standard Gaussian measure on $R^{n}$ . We prove that for every symmetric convex sets $K, L$ in $R^{n}$ and every $λ \in (0, 1)$ , $$γ_n(λK+(1-λ)L)^{\frac{1…

math.FA2020

On Pisier's inequality for UMD targets

Alexandros Eskenazis

We prove an extension of Pisier's inequality (1986) with a dimension independent constant for vector valued functions whose target spaces satisfy a relaxation of the UMD property.

math.FA2019

Polynomial inequalities on the Hamming cube

Alexandros Eskenazis, Paata Ivanisvili

Let $(X, ∥ \cdot ∥_{X})$ be a Banach space. The purpose of this article is to systematically investigate dimension independent properties of vector valued functions $f:\{-1,1\}^n\to X…

math.MG2018★ 5 cited

Nonpositive curvature is not coarsely universal

Alexandros Eskenazis, Manor Mendel, Assaf Naor

We prove that not every metric space embeds coarsely into an Alexandrov space of nonpositive curvature. This answers a question of Gromov (1993) and is in contrast to the fact that…

math.CA2018★ 4 cited

Dimension independent Bernstein-Markov inequalities in Gauss space

Alexandros Eskenazis, Paata Ivanisvili

We obtain the following dimension independent Bernstein-Markov inequality in Gauss space: for each $1 \leq p < \infty$ there exists a constant $C_{p} > 0$ such that for any $k \geq 1$ and…

math.MG2018★ 7 cited

On extremal sections of subspaces of $L_{p}$

Alexandros Eskenazis

Let $m, n \in N$ and $p \in (0, \infty)$ . For a finite dimensional quasi-normed space $X = (R^{m}, ∥ \cdot ∥_{X})$ , let $$B_p^n(X) = \Big\{ (x_1,\ldots,x_n)\in\big(\mathbb{R}…

math.PR2018

Cutoff for the Bernoulli-Laplace urn model with $o (n)$ swaps

Alexandros Eskenazis, Evita Nestoridi

We study the mixing time of the $(n, k)$ Bernoulli--Laplace urn model, where $k \in {0, 1, \dots, n}$ . Consider two urns, each containing $n$ balls, so that when combined they have pr…

The dimension-free threshold for maximal sections of ℓp​

Functional perimeter and the dimensional Brunn-Minkowski inequality for log-concave measures

An optimal algorithm for average distance in typical regular graphs

Concavity principles for weighted marginals

Approximation of polynomials from Walsh tail spaces

Some geometric applications of the discrete heat flow

On the entropy and information of Gaussian mixtures

Discrete logarithmic Sobolev inequalities in Banach spaces

Intrinsic dimensional functional inequalities on model spaces

Distributional stability of the Szarek and Ball inequalities

Resilience of cube slicing in ℓp​

Low-degree learning and the metric entropy of polynomials

Sharp Rosenthal-type inequalities for mixtures and log-concave variables

Average distortion embeddings, nonlinear spectral gaps, and a metric John theorem (after Assaf Naor)

Learning low-degree functions from a logarithmic number of random queries

Sharp growth of the Ornstein-Uhlenbeck operator on Gaussian tail spaces

Talagrand's influence inequality revisited

The dimensional Brunn-Minkowski inequality in Gauss space

On Pisier's inequality for UMD targets

Polynomial inequalities on the Hamming cube

Nonpositive curvature is not coarsely universal

Dimension independent Bernstein-Markov inequalities in Gauss space

On extremal sections of subspaces of Lp​

Cutoff for the Bernoulli-Laplace urn model with o(n) swaps

The dimension-free threshold for maximal sections of $ℓ_{p}$

Resilience of cube slicing in $ℓ_{p}$

On extremal sections of subspaces of $L_{p}$

Cutoff for the Bernoulli-Laplace urn model with $o (n)$ swaps