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

Abstract

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.

21 pages. To appear in J. Topol. Anal. This revision fixes a small error at the bottom of page 18, which was brought to my attention by Johel Beltran and Wilson Cabanillas