Haagerup's phase transition at polydisc slicing

Abstract

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 Euclidean spheres. This provides a probabilistic extension of the Oleszkiewicz-Pelczyński polydisc slicing result. The Haagerup-type phase transition occurs exactly when the p-norm recovers volume, in contrast to the real case. We also obtain partial results in higher dimensions.

Final version. To appear in Analysis & PDE

References in corpus (4)

• Transport-majorization to analytic and geometric inequalities
• Slicing ${\ell }_p$-balls reloaded: stability, planar sections in ${\ell }_1$
• Khinchin-type inequalities via Hadamard's factorisation
• Sharp bounds on $p$-norms for sums of independent uniform random variables, $0<p<1$