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

Mathematics – Probability

Scientific paper

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22 pages

Scientific paper

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.

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