P. Valettas

activity

20142025

most citedRandom version of Dvoretzky's theorem in

ℓ_{p}^{n}

24 citations · 36 across the 11 of their papers we have counts for

collaborators

15 papers

math.PR2025

A probabilistic approach to strong natural boundaries

Stamatis Dostoglou, Petros Valettas

We study the local non-extendability of random power series beyond their disk of convergence. We show that random power series formed by independent coefficients which are asymptot…

math.CV2024

On the clustering of Padé zeros and poles of random power series

Stamatis Dostoglou, Petros Valettas

We estimate non-asymptotically the probability of uniform clustering around the unit circle of the zeros of the $[m, n]$ -Padé approximant of a random power series $f(z) = \sum_{j=0}…

math.NA2022

Approximate Real Symmetric Tensor Rank

Alperen A. Ergür, Jesus Rebollo Bueno, Petros Valettas

We investigate the effect of an $ε$ -room of perturbation tolerance on symmetric tensor decomposition. To be more precise, suppose a real symmetric $d$ -tensor $f$ , a norm…

math.PR2021

Decompositions of finite high-dimensional random arrays

Pandelis Dodos, Konstantinos Tyros, Petros Valettas

A $d$ -dimensional random array on a nonempty set $I$ is a stochastic process $X = ⟨ X_{s} : s \in (d I) ⟩$ indexed by the set $(d I)$ of all $d$ -elem…

math.PR2021

Concentration estimates for functions of finite high-dimensional random arrays

Pandelis Dodos, Konstantinos Tyros, Petros Valettas

Let $X$ be a $d$ -dimensional random array on $[n]$ whose entries take values in a finite set $X$ , that is, $\boldsymbol{X}=\langle X_s:s\in \binom{[n]}{d}\ra…

math.FA2019

Hypercontractivity and Lower Deviation Estimates in Normed Spaces

Grigoris Paouris, Konstantin Tikhomirov, Petros Valettas

We consider the problem of estimating small ball probabilities $P {f (G) ⩽ δ E f (G)}$ for sub-additive,positively homogeneous functions $f$ with respect to th…

math.FA2017

Dichotomies, structure, and concentration in normed spaces

Grigoris Paouris, Petros Valettas

We use probabilistic, topological and combinatorial methods to establish the following deviation inequality: For any normed space $X = (R^{n}, ∥ \cdot ∥)$ there exists an inve…

math.PR2017

On the tightness of Gaussian concentration for convex functions

Petros Valettas

The concentration of measure phenomenon in Gauss' space states that every $L$ -Lipschitz map $f$ on $R^{n}$ satisfies \[ γ_{n} \left(\{ x : | f(x) - M_{f} | \geqslant t \} \ri…

math.FA2017

Variance estimates and almost Euclidean structure

Grigoris Paouris, Petros Valettas

We introduce and initiate the study of new parameters associated with any norm and any log-concave measure on $R^{n}$ , which provide sharp distributional inequalities. In the…

math.MG2017

On a quantitative reversal of Alexandrov's inequality

Grigoris Paouris, Peter Pivovarov, Petros Valettas

Alexandrov's inequalities imply that for any convex body $A$ , the sequence of intrinsic volumes $V_{1} (A), \dots, V_{n} (A)$ is non-increasing (when suitably normalized). Milman's random…

math.PR2016

A Gaussian small deviation inequality for convex functions

Grigoris Paouris, Petros Valettas

Let $Z$ be an $n$ -dimensional Gaussian vector and let $f : R^{n} \to R$ be a convex function. We show that: $$\mathbb P \left( f(Z) \leq \mathbb E f(Z) -t\sqrt{ {\rm V…

math.MG2016★ 11 cited

Inequalities for the surface area of projections of convex bodies

Apostolos Giannopoulos, Alexander Koldobsky, Petros Valettas

We provide general inequalities that compare the surface area S(K) of a convex body K in $R^{n}$ to the minimal, average or maximal surface area of its hyperplane or lower…

math.FA2015★ 1 cited

On Dvoretzky's theorem for subspaces of $L_{p}$

Grigoris Paouris, Petros Valettas

We prove that for any $2 < p < \infty$ and for every $n$ -dimensional subspace $X$ of $L_{p}$ , represented on $R^{n}$ , whose unit ball $B_{X}$ is in Lewis' position one has the follow…

math.FA2015★ 24 cited

Random version of Dvoretzky's theorem in $ℓ_{p}^{n}$

Grigoris Paouris, Petros Valettas, Joel Zinn

We study the dependence on $ε$ in the critical dimension $k (n, p, ε)$ for which one can find random sections of the $ℓ_{p}^{n}$ -ball which are $(1 + ε)$ -sp…

math.FA2014

Neighborhoods on the Grasmannian of marginals with bounded isotropic constant

Grigoris Paouris, Petros Valettas

We show that for any isotropic log-concave probability measure $μ$ on $R^{n}$ , for every $ε > 0$ , every $1 \leq k \leq n$ and any $E \in G_{n, k}$ there exist…

A probabilistic approach to strong natural boundaries

On the clustering of Padé zeros and poles of random power series

Approximate Real Symmetric Tensor Rank

Decompositions of finite high-dimensional random arrays

Concentration estimates for functions of finite high-dimensional random arrays

Hypercontractivity and Lower Deviation Estimates in Normed Spaces

Dichotomies, structure, and concentration in normed spaces

On the tightness of Gaussian concentration for convex functions

Variance estimates and almost Euclidean structure

On a quantitative reversal of Alexandrov's inequality

A Gaussian small deviation inequality for convex functions

Inequalities for the surface area of projections of convex bodies

On Dvoretzky's theorem for subspaces of Lp​

Random version of Dvoretzky's theorem in ℓpn​

Neighborhoods on the Grasmannian of marginals with bounded isotropic constant

On Dvoretzky's theorem for subspaces of $L_{p}$

Random version of Dvoretzky's theorem in $ℓ_{p}^{n}$