Abstract. Uniform probability distributions on ℓp 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.
A very detailed mathematical account of such a convergence has been given in REF starting from uniform distributions on the intersection of a simplex and a sphere.
A note about the uniform distribution on the intersection of a simplex and a sphere
arXiv: Probability
Mathematics