2 citations · 4 across the 22 of their papers we have counts for
31 papers
Blaschke--Santaló inequalities with respect to costs
Alexander V. Kolesnikov, Galyna V. Livshyts, Liran Rotem
We study functional Blaschke--Santaló inequalities in which the inner product is replaced by a cost. An inequality on each orthant, combined with Steiner symmetrization, gives a su…
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…
On p-Brunn-Minkowski and Brascamp-Lieb inequalities
Alexander V. Kolesnikov, Galyna Livshyts, Liran Rotem
We show that a strong version of the Brascamp--Lieb inequality for symmetric log-concave measure with -homogeneous potential is equivalent to a -Brunn--Minkowski inequali…
On the polar of Schneider's difference body
Julián Haddad, Dylan Langharst, Galyna V. Livshyts +1
In 1970, Schneider introduced the th-order extension of the difference body of a convex body , the convex body in . He conject…
On weighted Blaschke--Santalo and strong Brascamp--Lieb inequalities
Andrea Colesanti, Alexander Kolesnikov, Galyna Livshyts +1
In this paper, we study new extensions of the functional Blaschke-Santaló inequalities, and explore applications of such new inequalities beyond the classical setting of the standa…
The Brunn-Minkowski inequality for the first eigenvalue of the Ornstein-Uhlenbeck operator and log-concavity of the relevant eigenfunction
Andrea Colesanti, Elisa Francini, Galyna Livshyts +1
We prove that the first (nontrivial) Dirichlet eigenvalue of the Ornstein-Uhlenbeck operator as a function of the domain, is convex with r…
Stability and the equality case in the B-theorem
Orli Herscovici, Galyna V. Livshyts, Liran Rotem +1
In this paper, we show the stability, and characterize the equality cases in the strong B-inequality of Cordero-Erasquin, Fradelizi and Maurey \cite{B-conj}. As an application, we…
Kohler-Jobin meets Ehrhard: the sharp lower bound for the Gaussian principal frequency while the Gaussian torsional rigidity is fixed, via rearrangements
Orli Herscovici, Galyna V. Livshyts
In this note, we provide an adaptation of the Kohler-Jobin rearrangement technique to the setting of the Gauss space. As a result, we prove the Gaussian analogue of the Kohler-Jobi…
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…
New bounds on the minimal dispersion
Alexander E. Litvak, Galyna V. Livshyts
We provide a new construction for a set of boxes approximating axis-parallel boxes of fixed volume in . This improves upper bounds for the minimal dispersion of a point s…
A universal bound in the dimensional Brunn-Minkowski inequality for log-concave measures
Galyna V. Livshyts
We show that for any log-concave measure on , any pair of symmetric convex sets and , and any $$μ((1-λ) K+λL)^{c_n}\geq (1-λ) μ(K)^{c_n}+λμ(L…
On a conjectural symmetric version of Ehrhard's inequality
Galyna V. Livshyts
We formulate a plausible conjecture for the optimal Ehrhard-type inequality for convex symmetric sets with respect to the Gaussian measure. Namely, letting $J_{k-1}(s)=\int^s_0 t^{…
On the local version of the Log-Brunn-Minkowski conjecture and some new related geometric inequalities
Alexander V. Kolesnikov, Galyna V. Livshyts
We prove that for any semi-norm on and any symmetric convex body in \begin{equation}\label{ineq-abs2} \int_{\partial K} \frac{\|n_x\…
On the -Brunn-Minkowski and dimensional Brunn-Minkowski conjectures for log-concave measures
Johannes Hosle, Alexander V. Kolesnikov, Galyna V. Livshyts
We study several of the recent conjectures in regards to the role of symmetry in the inequalities of Brunn-Minkowski type, such as the -Brunn-Minkowski conjecture of Böröczky,…
Distribution of the minimal distance of random linear codes
Jing Hao, Han Huang, Galyna Livshyts +1
In this paper, we study the distribution of the minimal distance (in the Hamming metric) of a random linear code of dimension in . We provide quantitative estim…
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 $…
Some remarks about the maximal perimeter of convex sets with respect to probability measures
Galyna V. Livshyts
In this note we study the maximal perimeter of a convex set in with respect to various classes of measures. Firstly, we show that for a probability measure on $…
Remarks on the Rényi Entropy of a sum of IID random variables
Benjamin Jaye, Galyna V. Livshyts, Grigoris Paouris +1
In this note we study a conjecture of Madiman and Wang which predicted that the generalized Gaussian distribution minimizes the Rényi entropy of the sum of independent random varia…
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…
The lower bound for Koldobsky's slicing inequality via random rounding
Bo'az Klartag, Galyna V. Livshyts
We study the lower bound for Koldobsky's slicing inequality. We show that there exists a measure and a symmetric convex body , such that for all $ξ\in…
On the Gardner-Zvavitch conjecture: symmetry in the inequalities of Brunn-Minkowski type
Alexander V. Kolesnikov, Galyna V. Livshyts
In this paper, we study the conjecture of Gardner and Zvavitch from \cite{GZ}, which suggests that the standard Gaussian measure enjoys -concavity with respect to…
Cube is a strict local maximizer for the illumination number
Galyna Livshyts, Konstantin Tikhomirov
It was conjectured by Levi, Hadwiger, Gohberg and Markus that the boundary of any convex body in can be illuminated by at most light sources, and, moreover, $…
A note on the quantitative local version of the log-Brunn-Minkowski inequality
Andrea Colesanti, Galyna V. Livshyts
We prove that the log-Brunn-Minkowski inequality \begin{equation*} |λK+_0 (1-λ)L|\geq |K|^λ|L|^{1-λ} \end{equation*} (where is the Lebesgue measure and is the so-ca…
An extension of Minkowski's theorem and its applications to questions about projections for measures
Galyna V. Livshyts
Minkowski's Theorem asserts that every centered measure on the sphere which is not concentrated on a great subsphere is the surface area measure of some convex body, and, moreover,…