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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Showing 2010Show all

2 papers · 1 filter

math.PR2010

Sharp bounds on the rate of convergence of the empirical covariance matrix

Radosław Adamczak, Alexander E. Litvak, Alain Pajor +1

Let $X_{1}, ..., X_{N} \in R^{n}$ be independent centered random vectors with log-concave distribution and with the identity as covariance matrix. We show that with overwhelming probabilit…

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…

Sharp bounds on the rate of convergence of the empirical covariance matrix

The Gelfand widths of ℓp​-balls for 0<p≤1

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