A. Pajor

activity

19922016

most citedQuantitative estimates of the convergence of the empirical covariance matrix in Log-concave Ensembles

117 citations · 296 across the 16 of their papers we have counts for

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5 papers · 1 filter

math.FA2013

Thin-shell concentration for convex measures

Matthieu Fradelizi, Olivier Guédon, Alain Pajor

We prove that for $s < 0$ , $s$ -concave measures on $R^{n}$ satisfy a thin shell concentration similar to the log-concave one. It leads to a Berry-Esseen type estimate for the…

math.FA2010★ 43 cited

The Gelfand widths of $ℓ_{p}$ -balls for $0 < p \leq 1$

Simon Foucart, Alain Pajor, Holger Rauhut +1

We provide sharp lower and upper bounds for the Gelfand widths of $ℓ_{p}$ -balls in the $N$ -dimensional $ℓ_{q}^{N}$ -space for $0 < p \leq 1$ and $p < q \leq 2$ . Such estimates are highly…

math.FA2008

Majorizing measures and proportional subsets of bounded orthonormal systems

Olivier Guedon, Shahar Mendelson, Alain Pajor +1

In this article we prove that for any orthonormal system $(\vphi_j)_{j=1}^n \subset L_2$ that is bounded in $L_{\infty}$ , and any $1 < k < n$ , there exists a subset $I$ of cardinali…

math.FA2006

A note on subgaussian estimates for linear functionals on convex bodies

Apostolos Giannopoulos, Alain Pajor, Grigoris Paouris

We give an alternative proof of a recent result of Klartag on the existence of almost subgaussian linear functionals on convex bodies. If $K$ is a convex body in $R^{n}$ wi…

math.FA2005★ 29 cited

Reconstruction and subgaussian operators

Shahar Mendelson, Alain Pajor, Nicole Tomczak-Jaegermann

We present a randomized method to approximate any vector $v$ from some set $T \subset R^{n}$ . The data one is given is the set $T$ , and $k$ scalar products $(\inr{X_i,v})_{i=1}^k$,…