2 citations · 4 across the 22 of their papers we have counts for
6 papers · 1 filter
On the Smallest Singular Value of Log-Concave Random Matrices
Manuel Fernandez, Galyna V. Livshyts, Stephanie Mui
Let be an random matrix whose entries are coordinates of an isotropic log-concave random vector in . We prove sharp lower tail estimates for the sm…
Asymptotic Bounds on the Combinatorial Diameter of Random Polytopes
Gilles Bonnet, Daniel Dadush, Uri Grupel +2
The combinatorial diameter of a polytope is the maximum shortest path distance between any pair of vertices. In this paper, we provide upper and lower…
The smallest singular value of inhomogeneous square random matrices
Galyna V. Livshyts, Konstantin Tikhomirov, Roman Vershynin
We show that for an random matrix with independent uniformly anti-concentrated entries, such that , the smallest singular value $…
The smallest singular value of heavy-tailed not necessarily i.i.d. random matrices via random rounding
Galyna V. Livshyts
We are concerned with the small ball behavior of the smallest singular value of random matrices. Often, establishing such results involves, in some capacity, a discretization of th…
On sharp bounds for marginal densities of product measures
Galyna Livshyts, Grigoris Paouris, Peter Pivovarov
We discuss optimal constants in a recent result of Rudelson and Vershynin on marginal densities. We show that if is a probability density on of the form $f(x)=\prod_{i=1…
On the Brunn-Minkowski inequality for general measures with applications to new isoperimetric-type inequalities
Galyna Livshyts, Arnaud Marsiglietti, Piotr Nayar +1
In this paper we present new versions of the classical Brunn-Minkowski inequality for different classes of measures and sets. We show that the inequality \[ μ(λA + (1-λ)B)^{1/n} \g…