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

Showing math.FAShow all

6 papers · 1 filter

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.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.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…

Hypercontractivity and Lower Deviation Estimates in Normed Spaces

Dichotomies, structure, and concentration in normed spaces

Variance estimates and almost Euclidean structure

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 $ℓ_{p}^{n}$