Minimal angle spread in the probability simplex with respect to the uniform distribution

TL;DR

This paper analytically determines the minimal angle spread in the probability simplex relative to the uniform distribution, revealing it diminishes to zero as the dimension increases, with applications in cognitive science.

Contribution

It provides an explicit formula for the minimal angle spread in the probability simplex and analyzes its asymptotic behavior as the dimension grows.

Findings

Minimal angle spread approaches zero in high dimensions

Analytical solution to the optimization problem

Application discussed in cognitive science

Abstract

We compute the minimal angle spread with respect to the uniform distribution in the probability simplex. The resulting optimization problem is analytically solved. The formula provided shows that the minimal angle spread approaches zero as the dimension tends to infinity. We also discuss an application in cognitive science.