A note about the uniform distribution on the intersection of a simplex and a sphere

Sourav Chatterjee

Published 2010-11-17, updated 2016-05-01Version 2

Uniform probability distributions on $\ell_p$ balls and spheres have been studied extensively and are known to behave like product measures in high dimensions. In this note we consider the uniform distribution on the intersection of a simplex and a sphere. Certain new and interesting features, such as phase transitions and localization phenomena emerge.