52 citations · 180 across the 41 of their papers we have counts for
7 papers · 1 filter
Typical values of extremal-weight combinatorial structures with independent symmetric weights
Yun Cheng, Yixue Liu, Tomasz Tkocz +1
Suppose that the edges of a complete graph are assigned weights independently at random and we ask for the weight of the minimal-weight spanning tree, or perfect matching, or Hamil…
Resilience of cube slicing in
Alexandros Eskenazis, Piotr Nayar, Tomasz Tkocz
Ball's celebrated cube slicing (1986) asserts that among hyperplane sections of the cube in , the central section orthogonal to has the greatest vol…
Extremal sections and projections of certain convex bodies: a survey
Piotr Nayar, Tomasz Tkocz
We survey results concerning sharp estimates on volumes of sections and projections of certain convex bodies, mainly balls, by and onto lower dimensional subspaces. This s…
Complex Hanner's Inequality for Many Functions
Jonathan Jenkins, Tomasz Tkocz
We establish Hanner's inequality for arbitrarily many functions in the setting where the Rademacher distribution is replaced with higher dimensional random vectors uniform on Eucli…
Haagerup's phase transition at polydisc slicing
Giorgos Chasapis, Salil Singh, Tomasz Tkocz
We establish a sharp comparison inequality between the negative moments and the second moment of the magnitude of sums of independent random vectors uniform on three-dimensional Eu…
Sharp Rosenthal-type inequalities for mixtures and log-concave variables
Giorgos Chasapis, Alexandros Eskenazis, Tomasz Tkocz
We obtain Rosenthal-type inequalities with sharp constants for moments of sums of independent random variables which are mixtures of a fixed distribution. We also identify extremis…