52 citations · 180 across the 41 of their papers we have counts for
7 papers · 1 filter
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…
Probabilistic analysis of algorithms for cost constrained minimum weighted combinatorial objects
Alan Frieze, Tomasz Tkocz
We consider cost constrained versions of the minimum spanning tree problem and the assignment problem. We assume edge weights are independent copies of a continuous random variable…
Shortest paths with a cost constraint: a probabilistic analysis
Alan Frieze, Tomasz Tkocz
We consider a constrained version of the shortest path problem on the complete graphs whose edges have independent random lengths and costs. We establish the asymptotic value of th…
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…
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…
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…