Labrini Hioni

collaborators

3 papers

math.MG2016

Asymptotic shape of the convex hull of isotropic log-concave random vectors

Apostolos Giannopoulos, Labrini Hioni, Antonis Tsolomitis

Let $x_{1}, \dots, x_{N}$ be independent random points distributed according to an isotropic log-concave measure $μ$ on $R^{n}$ , and consider the random polytope $$K_N:={\rm co…

math.MG2016

Geometry of random sections of isotropic convex bodies

Apostolos Giannopoulos, Labrini Hioni, Antonis Tsolomitis

Let $K$ be an isotropic symmetric convex body in $R^{n}$ . We show that a subspace $F \in G_{n, n - k}$ of codimension $k = γ n$ , where $γ \in (1/ n, 1)$ , satisfies $$K\cap F\s…

math.MG2015

Random approximation and the vertex index of convex bodies

Silouanos Brazitikos, Giorgos Chasapis, Labrini Hioni

We prove that there exists an absolute constant $α > 1$ with the following property: if $K$ is a convex body in $R^{n}$ whose center of mass is at the origin, then a random s…