Khinchin inequalities for uniforms on spheres with a deficit

2025/06/27 by Jakimiuk, Jacek, Tang, Colin, Tkocz, Tomasz
#FOS: Mathematics #Functional Analysis (math.FA) #Primary 60E15 #Probability (math.PR) #Secondary 26D15

paper · doi:10.48550/arxiv.2506.22040

Abstract

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).

Citations

• From simplex slicing to sharp reverse Hölder inequalities
• On the optimal L_p-L₄ Khintchine inequality
• Stability of Khintchine inequalities with optimal constants between the second and the p-th moment for p ≥ 3
• Stability of simplex slicing
• The centered convex body whose marginals have the heaviest tails
• A robust Khintchine inequality, and algorithms for computing optimal constants in Fourier analysis and high-dimensional geometry
• Extremal Probabilistic Problems and Hotelling's T² Test Under Symmetry Condition

Related

• Sums of norm spheres are norm shells and lower triangle inequalities are sharp
• The best constant in the Khintchine inequality of the Orlicz space L_ψ2 for equidistributed random variables on spheres
• Multidimensional probability inequalities via spherical symmetry
• Spheres and Minima
• On the optimal L_p-L₄ Khintchine inequality