Large deviations for uniform projections of $p$-radial distributions on $\ell_p^n$-balls

Abstract

We consider products of uniform random variables from the Stiefel manifold of orthonormal kframes in R, k ≤ n, and random vectors from the n-dimensional lp -ball B n p with certain pradial distributions, p ∈ [1,∞). The distribution of this product geometrically corresponds to the projection of the p-radial distribution on Bp onto a random k-dimensional subspace. We derive large deviation principles (LDPs) on the space of probability measures on R for sequences of such projections.