52 citations · 180 across the 41 of their papers we have counts for
5 papers · 1 filter
Stability of polydisc slicing
Nathaniel Glover, Tomasz Tkocz, Katarzyna Wyczesany
We prove a dimension-free stability result for polydisc slicing due to Oleszkiewicz and Pelczyński (2000). Intriguingly, compared to the real case, there is an additional asymptoti…
A note on volume thresholds for random polytopes
Debsoumya Chakraborti, Tomasz Tkocz, Beatrice-Helen Vritsiou
We study the expected volume of random polytopes generated by taking the convex hull of independent identically distributed points from a given distribution. We show that for log-c…
A note on the extremal noncentral sections of the cross-polytope
Ruoyuan Liu, Tomasz Tkocz
We find minimal and maximal length of intersections of lines at a fixed distance to the origin with the cross-polytope. We also find maximal volume noncentral sections of the cross…
Improved bounds for Hadwiger's covering problem via thin-shell estimates
Han Huang, Boaz A. Slomka, Tomasz Tkocz +1
A central problem in discrete geometry, known as Hadwiger's covering problem, asks what the smallest natural number is such that every convex body in ${\mathbb R}…
On a convexity property of sections of the cross-polytope
Piotr Nayar, Tomasz Tkocz
We establish the log-concavity of the volume of central sections of dilations of the cross-polytope (the strong B-inequality for the cross-polytope and Lebesgue measure restricted…