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Autor: Bárány, I., Csóka, E., Károlyi, Gy., Tóth, G.

Given a sequence $S=(s_1,\dots,s_m) \in [0, 1]^m$, a block $B$ of $S$ is a subsequence $B=(s_i,s_{i+1},\dots,s_j)$. The size $b$ of a block $B$ is the sum of its elements. It is proved in [1] that for each positive integer $n$, there is a partition o

Externí odkaz: http://arxiv.org/abs/1706.06095

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A fractional Helly theorem for boxes

Autor: Bárány, I., Fodor, F., Martínez-Pérez, A., Montejano, L., Oliveros, D., Pór, A.

Publikováno v: Computational Geometry: Theory and Applications 48 (2015), no. 3, 221-224

Let $\mathcal{F}$ be a family of $n$ axis-parallel boxes in $\mathbb{R}^d$ and $\alpha\in (1-1/d,1]$ a real number. There exists a real number $\beta(\alpha )>0$ such that if there are $\alpha {n\choose 2}$ intersecting pairs in $\mathcal{F}$, then $

Externí odkaz: http://arxiv.org/abs/1410.0467

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Akademický článek

Smaller Gershgorin disks for multiple eigenvalues of complex matrices.

Autor: Bárány, I.^1,2 (AUTHOR) barany@renyi.hu, Solymosi, J.^3,4 (AUTHOR)

Publikováno v: Acta Mathematica Hungarica. Feb2023, Vol. 169 Issue 1, p289-300. 12p.

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Central limit theorems for Gaussian polytopes

Autor: Barany, I., Vu, V. H.

Choose $n$ random, independent points in $\R^d$ according to the standard normal distribution. Their convex hull $K_n$ is the {\sl Gaussian random polytope}. We prove that the volume and the number of faces of $K_n$ satisfy the central limit theorem,

Externí odkaz: http://arxiv.org/abs/math/0610192

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