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Large deviations for uniform projections of p-radial distributions on lnp - balls

Kaufmann Tom, Sambale Holger, Thäle Christoph

Probability and Mathematical Statistics

2022

Vol. 42, Fasc. 2

303--317

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