52 citations · 180 across the 41 of their papers we have counts for
4 papers · 2 filters
From Ball's cube slicing inequality to Khinchin-type inequalities for negative moments
Giorgos Chasapis, Hermann König, Tomasz Tkocz
We establish a sharp moment comparison inequality between an arbitrary negative moment and the second moment for sums of independent uniform random variables, which extends Ball's…
Reversals of Rényi Entropy Inequalities under Log-Concavity
James Melbourne, Tomasz Tkocz
We establish a discrete analog of the Rényi entropy comparison due to Bobkov and Madiman. For log-concave variables on the integers, the min entropy is within log e of the usual Sh…
Random volumes in d-dimensional polytopes
Alan Frieze, Wesley Pegden, Tomasz Tkocz
Suppose we choose points uniformly randomly from a convex body in dimensions. How large must be, asymptotically with respect to , so that the convex hull of the poin…
Log-concavity and log-convexity of moments of averages of i.i.d. random variables
Philip Lamkin, Tomasz Tkocz
We show that the sequence of moments of order less than 1 of averages of i.i.d. positive random variables is log-concave. For moments of order at least 1, we conjecture that the se…