2 citations · 4 across the 22 of their papers we have counts for
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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^{…