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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…
math.PR2025
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).