We show that, for an n× n random matrix A with independent uniformly anticoncentrated
entries such that E‖ A‖ HS 2≤ K n 2, the smallest singular value σ n (A) of A satisfies P {σ …

We develop a unified approach to bounding the largest and smallest singular values of an
inhomogeneous random rectangular matrix, based on the non-backtracking operator and …

We show the existence of a net near the sphere, such that the values of any matrix on the
sphere and on the net are compared via a regularized Hilbert-Schmidt norm, which we …

The reader will have noticed the non-standard appearance of this piece. Indeed, we are
used to reading papers which are either survey papers or research ones (or a mixture of …

For ad-dimensional random vector X, let pn, X (θ) be the probability that the convex hull of n
independent copies of X contains a given point θ. We provide several sharp inequalities …

We investigate the asymptotic properties of random polytopes arising as convex hulls of $ n
$ independent random points sampled from a family of block-beta distributions. Notably, this …

We study the geometry of centrally symmetric random polytopes, generated by N
independent copies of a random vector X taking values in ℝ n. We show that under minimal …

Let $ X=(x_ {ij})\in\mathbb {R}^{N\times n} $ be a rectangular random matrix with iid entries
(we assume $ N/n\to\mathbf {a}> 1$), and denote by $\sigma_ {min}(X) $ its smallest …

We prove new results about the robustness of noise-blind decoders for the problem of
reconstructing a sparse vector from underdetermined linear measurements. Our results …

For a d-dimensional random vector X, let pn, X (θ) be the probability that the convex hull of n
independent copies of X contains a given point θ. We provide several sharp inequalities …