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

2022/03/01 by Tom L. Kaufmann, Kaufmann, Tom, Holger Sambale +3
Mathematics · #Advanced Harmonic Analysis Research

paper · pdf · doi:10.48550/arxiv.2203.00476

Abstract

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 ℓ_pⁿ-ball \mathbbB_pⁿ with certain p-radial distributions, p∈[1,∞). The distribution of this product geometrically corresponds to the projection of the p-radial distribution on \mathbbBⁿ_p onto a random k-dimensional subspace. We derive large deviation principles (LDPs) on the space of probability measures on ℝ^k for sequences of such projections.

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