52 citations · 180 across the 41 of their papers we have counts for
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Tail bounds for sums of independent two-sided exponential random variables
Jiawei Li, Tomasz Tkocz
We establish upper and lower bounds with matching leading terms for tails of weighted sums of two-sided exponential random variables. This extends Janson's recent results for one-s…
Slicing -balls reloaded: stability, planar sections in
Giorgos Chasapis, Piotr Nayar, Tomasz Tkocz
We show that the two-dimensional minimum-volume central section of the -dimensional cross-polytope is attained by the regular -gon. We establish stability-type results for h…
Rademacher-Gaussian tail comparison for complex coefficients and related problems
Giorgos Chasapis, Ruoyuan Liu, Tomasz Tkocz
We provide a generalisation of Pinelis' Rademacher-Gaussian tail comparison to complex coefficients. We also establish uniform bounds on the probability that the magnitude of weigh…
Sharp bounds on -norms for sums of independent uniform random variables,
Giorgos Chasapis, Keerthana Gurushankar, Tomasz Tkocz
We provide a sharp lower bound on the -norm of a sum of independent uniform random variables in terms of its variance when . We address an analogous question for -…
Khinchin-type inequalities via Hadamard's factorisation
Alex Havrilla, Piotr Nayar, Tomasz Tkocz
We prove Khinchin-type inequalities with sharp constants for type L random variables and all even moments. Our main tool is Hadamard's factorisation theorem from complex analysis,…