17 citations · 41 across the 10 of their papers we have counts for
7 papers · 1 filter
On Sections of Convex Bodies in John's Position and of Generalised Balls
David Alonso-Gutiérrez, Silouanos Brazitikos, Giorgos Chasapis
We revisit an ingenious argument of K. Ball to provide sharp estimates for the volume of sections of a convex body in John's position. Our technique combines the geometric Brascamp…
Affine quermassintegrals of random polytopes
Giorgos Chasapis, Nikos Skarmogiannis
A question related to some conjectures of Lutwak about the affine quermassintegrals of a convex body in asks whether for every convex body in ${\mathbb R}^n…
Norms of weighted sums of log-concave random vectors
Giorgos Chasapis, Apostolos Giannopoulos, Nikos Skarmogiannis
Let and be centrally symmetric convex bodies of volume in . We provide upper bounds for the multi-integral expression \begin{equation*}\|{\bf t}\|_{C^s,K…
A note on norms of signed sums of vectors
Giorgos Chasapis, Nikos Skarmogiannis
Our starting point is an improved version of a result of D. Hajela related to a question of Komlós: we show that if is a function such that $\lim\limits_{n\to\infty }f(n)=\i…
Threshold phenomena for high-dimensional random polytopes
Gilles Bonnet, Giorgos Chasapis, Julian Grote +2
Let , , be independent random points in , distributed according to the so-called beta or beta-prime distribution, respectively. We establish thre…
Estimates for measures of lower dimensional sections of convex bodies
Giorgos Chasapis, Apostolos Giannopoulos, Dimitris-Marios Liakopoulos
We present an alternative approach to some results of Koldobsky on measures of sections of symmetric convex bodies, which allows us to extend them to the not necessarily symmetric…
Random approximation and the vertex index of convex bodies
Silouanos Brazitikos, Giorgos Chasapis, Labrini Hioni
We prove that there exists an absolute constant with the following property: if is a convex body in whose center of mass is at the origin, then a random s…