52 citations · 180 across the 41 of their papers we have counts for
30 papers · 1 filter
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…
Distributional stability of the Szarek and Ball inequalities
Alexandros Eskenazis, Piotr Nayar, Tomasz Tkocz
We prove an extension of Szarek's optimal Khinchin inequality (1976) for distributions close to the Rademacher one, when all the weights are uniformly bounded by a fract…
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…
Entropies of sums of independent gamma random variables
Giorgos Chasapis, Salil Singh, Tomasz Tkocz
We establish several Schur-convexity type results under fixed variance for weighted sums of independent gamma random variables and obtain nonasymptotic bounds on their Rényi entrop…
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…
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,…
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…
Sharp Khinchin-type inequalities for symmetric discrete uniform random variables
Alex Havrilla, Tomasz Tkocz
We establish several optimal moment comparison inequalities (Khinchin-type inequalities) for weighted sums of independent identically distributed symmetric discrete random variable…
Comparison of moments of Rademacher chaoses
Paata Ivanisvili, Tomasz Tkocz
We show that complex hypercontractivity gives better constants than real hypercontractivity in comparison inequalities for (low) moments of Rademacher chaoses (homogeneous polynomi…
Stochastic dominance and weak concentration for sums of independent symmetric random vectors
Witold Bednorz, Tomasz Tkocz
Kwapien and Woyczynski asked in their monograph (1992) whether their notion of superstrong domination is inherited when taking sums of independent symmetric random vectors (one vec…
On the convex infimum convolution inequality with optimal cost function
Marta Strzelecka, Michał Strzelecki, Tomasz Tkocz
We show that every symmetric random variable with log-concave tails satisfies the convex infimum convolution inequality with an optimal cost function (up to scaling). As a result,…
Gaussian mixtures: entropy and geometric inequalities
Alexandros Eskenazis, Piotr Nayar, Tomasz Tkocz
A symmetric random variable is called a Gaussian mixture if it has the same distribution as the product of two independent random variables, one being positive and the other a stan…
A multidimensional analogue of the Rademacher-Gaussian tail comparison
Piotr Nayar, Tomasz Tkocz
We prove a dimension-free tail comparison between the Euclidean norms of sums of independent random vectors uniformly distributed in centred Euclidean spheres and properly rescaled…
A reverse entropy power inequality for log-concave random vectors
Keith Ball, Piotr Nayar, Tomasz Tkocz
We prove that the exponent of the entropy of one dimensional projections of a log-concave random vector defines a 1/5-seminorm. We make two conjectures concerning reverse entropy p…
A note on suprema of canonical processes based on random variables with regular moments
Rafał Latała, Tomasz Tkocz
We derive two-sided bounds for expected values of suprema of canonical processes based on random variables with moments growing regularly. We also discuss a Sudakov-type minoration…
Two-sided bounds for -norms of combinations of products of independent random variables
Ewa Damek, Rafał Latała, Piotr Nayar +1
We show that for every positive p, the L_p-norm of linear combinations (with scalar or vector coefficients) of products of i.i.d. random variables, whose moduli have a nondegenerat…
Convex Poincaré inequality
P. Nayar, T. Tkocz
We characterize the symmetric measures which satisfy the one dimensional convex Poincaré inequality. For these measures the tenesorization argument yields concentration inequalitie…
A note on certain convolution operators
Piotr Nayar, Tomasz Tkocz
In this note we consider a certain class of convolution operators acting on the L_p spaces of the one dimensional torus. We prove that the identity minus such an operator is nicely…