Tomasz Tkocz

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math.PR2026

Khinchin inequalities for uniforms on spheres with a deficit

Jacek Jakimiuk, Colin Tang, Tomasz Tkocz

We sharpen the moment comparison inequalities with sharp constants for sums of random vectors uniform on Euclidean spheres, providing a deficit term (optimal in high dimensions).

math.PR2026

Moments of sums of exponentials, beyond CHS

Silouanos Brazitikos, Colin Tang, Tomasz Tkocz

We establish a sharp lower bound on the $L_{p}$ -norm of sums of independent exponential random variables with fixed variance, for $p \geq 2$ , thus extending Hunter's positivity theor…

math.PR2025

Negative Moments of Steinhaus Sums

Martin Rapaport, Tomasz Tkocz, Isabella Wu

We prove a sharp upper bound on negative moments of sums of independent Steinhaus random variables (that is uniform on circles in the plane). Together with the series of earlier wo…