Add to ORKGAbstract. We study two properties of random high dimensional sec-tions of convex bodies. In the first part of the paper we estimate the central section function |K ∩F⊥|1/kn−k for random F ∈ Gn,k and K ⊂ Rn a centrally symmetric isotropic convex body. This partially answers a question raised by V. Milman and A. Pajor (see [MP], p.88). In the sec-ond part we show that every symmetric convex body has random high dimensional sections F ∈ Gn,k with outer volume ratio bounded by ovr(K ∩ F) ≤ C n n − k lo
Existence of nicely bounded sections of two symmetric convex bodies K and L implies that th...
Existence of nicely bounded sections of two symmetric convex bodies K and L implies that th...
The main theme of this Ph.D. Thesis is the use of probabilistic methods in the theory of high-dimens...
Abstract. We study two properties of random high dimensional sec-tions of convex bodies. In the firs...
AbstractWe study two properties of random high dimensional sections of convex bodies. In the first p...
AbstractWe study two properties of random high dimensional sections of convex bodies. In the first p...
Abstract. Let K ⊂ Rn be a centrally symmetric isotropic convex body. We prove that for random F ∈ Gn...
In this paper we study geometry of compact, not necessarily centrally sym-metric, convex bodies in R...
We study the diameters of sections of convex bodies in RN de-termined by a random N × n matrix Γ, ei...
AbstractWe study the diameters of sections of convex bodies in RN determined by a random N×n matrix ...
AbstractSharpening work of the first two authors, for every proportion λ∈(0,1) we provide exact quan...
AbstractLet K be an isotropic convex body in Rn and let Zq(K) be the Lq-centroid body of K. For ever...
Let X1,..., XN be independent random vectors uniformly dis-tributed on an isotropic convex body K ⊂ ...
Let X1,…,XN be independent random vectors uniformly distributed on an isotropic convex body K ⊂ Rn, ...
AbstractFor convex bodies K with C2 boundary in Rd, we explore random polytopes with vertices chosen...
Existence of nicely bounded sections of two symmetric convex bodies K and L implies that th...
Existence of nicely bounded sections of two symmetric convex bodies K and L implies that th...
The main theme of this Ph.D. Thesis is the use of probabilistic methods in the theory of high-dimens...
Abstract. We study two properties of random high dimensional sec-tions of convex bodies. In the firs...
AbstractWe study two properties of random high dimensional sections of convex bodies. In the first p...
AbstractWe study two properties of random high dimensional sections of convex bodies. In the first p...
Abstract. Let K ⊂ Rn be a centrally symmetric isotropic convex body. We prove that for random F ∈ Gn...
In this paper we study geometry of compact, not necessarily centrally sym-metric, convex bodies in R...
We study the diameters of sections of convex bodies in RN de-termined by a random N × n matrix Γ, ei...
AbstractWe study the diameters of sections of convex bodies in RN determined by a random N×n matrix ...
AbstractSharpening work of the first two authors, for every proportion λ∈(0,1) we provide exact quan...
AbstractLet K be an isotropic convex body in Rn and let Zq(K) be the Lq-centroid body of K. For ever...
Let X1,..., XN be independent random vectors uniformly dis-tributed on an isotropic convex body K ⊂ ...
Let X1,…,XN be independent random vectors uniformly distributed on an isotropic convex body K ⊂ Rn, ...
AbstractFor convex bodies K with C2 boundary in Rd, we explore random polytopes with vertices chosen...
Existence of nicely bounded sections of two symmetric convex bodies K and L implies that th...
Existence of nicely bounded sections of two symmetric convex bodies K and L implies that th...
The main theme of this Ph.D. Thesis is the use of probabilistic methods in the theory of high-dimens...