3 papers
math.PR2026
A Sharp Gaussian Tail Bound for Sums of Uniforms
Xinjie He, Tomasz Tkocz, Katarzyna Wyczesany
We prove that the tail probabilities of sums of independent uniform random variables, up to a multiplicative constant, are dominated by the Gaussian tail with matching variance and…
math.PR2025
A Rényi entropy interpretation of anti-concentration and noncentral sections of convex bodies
James Melbourne, Tomasz Tkocz, Katarzyna Wyczesany
We extend Bobkov and Chistyakov's (2015) upper bounds on concentration functions of sums of independent random variables to a multivariate entropic setting. The approach is based o…
math.MG2024
Stability of polydisc slicing
Nathaniel Glover, Tomasz Tkocz, Katarzyna Wyczesany
We prove a dimension-free stability result for polydisc slicing due to Oleszkiewicz and PelczyÅski (2000). Intriguingly, compared to the real case, there is an additional asymptot…