Work

Haagerup’s phase transition at polydisc slicing

Year: 2024

Type: article

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.

Source: Analysis & PDE

DOI: 10.2140/apde.2024.17.2509

Authors: Giorgos Chasapis, Salil Singh, Tomasz Tkocz

Institutions: University of Crete, Carnegie Mellon University

Language: English

Topic: Point processes and geometric inequalities

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Funders: National Science Foundation, University of Crete, Hellenic Foundation for Research and Innovation

Awards: Analytic, Geometric, and Probabilistic Aspects of High-Dimensional Phenomena, Βάσεις Fourier και Διακριτή Γεωμετρία