APAlain Pajor
Alain Pajor
*This is an algorithmically generated author record based on publicly available information.
Alain Pajor has a total of 5 co-authors. Here are the top co-authors by number of shared publications:
- Olivier Guédon
Laboratoire d'Analyse et de Mathématiques Appliquées Université Paris-Est-Marne la Vallée 77454 Marne la Vallée O. G. : CEDEX 2 France
2 shared publications - Alexander E. Litvak
University of Alberta
1 shared publication - Alexander Koldobsky
Department of Mathematics, University of Missouri, Columbia, USA
1 shared publication - Matthieu Fradelizi
LAMA ( UMR 8050) Université Paris-Est UPEM UPEC CNRS F-77454 Marne-la-Valle FRANCE
1 shared publication - Nicole Tomczak-Jaegermann
University of Alberta
1 shared publication
Latest Publications
- Open Access
A remark on measures of sections of $L_p$-balls
We show that the slicing problem holds true for subspaces of $L_p,p>2$ in the setting of arbitrary measures in place of volume. This generalizes a result of Milman for the original slicing problem.Open AccessA remark on measures of sections of $L_p$-balls
We show that the slicing problem holds true for subspaces of $L_p,p>2$ in the setting of arbitrary measures in place of volume. This generalizes a result of Milman for the original slicing problem. - Open Access
On the interval of fluctuation of the singular values of random matrices
Let $A$ be a matrix whose columns $X_1,\dots, X_N$ are independent random vectors in $\mathbb{R}^n$. Assume that the tails of the 1-dimensional marginals decay as $\mathbb{P}(|\langle X_i, a\rangle|\geq t)\leq t^{-p}$ uniformly in $a\in S^{n-1}$ and $i\leq N$. Then for $p>4$ we prove that with high probability $A/{\sqrt{n}}$ has the Restricted Isometry Property (RIP) provided that Euclidean norms $|X_i|$ are concentrated around $\sqrt{n}$. We also show that the covariance matrix is well approximated by the empirical covariance matrix and establish corresponding quantitative estimates on the rate of convergence in terms of the ratio $n/N$. Moreover, we obtain sharp bounds for both problems when the decay is of the type $ \exp({-t^{\alpha}})$ with $\alpha \in (0,2]$, extending the known case $\alpha\in[1, 2]$.Open AccessOn the interval of fluctuation of the singular values of random matrices
Let $A$ be a matrix whose columns $X_1,\dots, X_N$ are independent random vectors in $\mathbb{R}^n$. Assume that the tails of the 1-dimensional marginals decay as $\mathbb{P}(|\langle X_i, a\rangle|\geq t)\leq t^{-p}$ uniformly in $a\in S^{n-1}$ and $i\leq N$. Then for $p>4$ we prove that with high probability $A/{\sqrt{n}}$ has the Restricted Isometry Property (RIP) provided that Euclidean norms $|X_i|$ are concentrated around $\sqrt{n}$. We also show that the covariance matrix is well approximated by the empirical covariance matrix and establish corresponding quantitative estimates on the rate of convergence in terms of the ratio $n/N$. Moreover, we obtain sharp bounds for both problems when the decay is of the type $ \exp({-t^{\alpha}})$ with $\alpha \in (0,2]$, extending the known case $\alpha\in[1, 2]$. - Open Access
Thin-shell concentration for convex measures
We prove that for $s<0$, $s$-concave measures on ${\mathbb R}^n$ satisfy a thin shell concentration similar to the log-concave one. It leads to a Berry-Esseen type estimate for their one dimensional marginal distributions. We also establish sharp reverse H\"older inequalities for $s$-concave measures.Open AccessThin-shell concentration for convex measures
We prove that for $s<0$, $s$-concave measures on ${\mathbb R}^n$ satisfy a thin shell concentration similar to the log-concave one. It leads to a Berry-Esseen type estimate for their one dimensional marginal distributions. We also establish sharp reverse H\"older inequalities for $s$-concave measures.