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

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5 papers · 1 filter

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.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.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.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…