For the full family of \u2113_p(n) spheres with 1 \u2264 p \u2264 \u221e, the coordinate distribution converges at rate \u221an and is described by weak convergence of a normalized empirical process to a limiting Gaussian process built from a Brownian bridge and a simple normal process.

From Asymptotic Distribution of Coordinates on High Dimensional Spheres · Confidence 0.98