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Contents of PMS, Vol. 42, Fasc. 2,
pages 303 - 317
DOI: 10.37190/0208-4147.00084
Published online 1.12.2022
 

Large deviations for uniform projections of p-radial distributionon on lpn-Balls

T. Kaufmann
H. Sambale
C. Thäle

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 lpn-balls Bpn with certain p-radial distributions, p ∈ [1,∞ ). The distribution of this product geometrically corresponds to the projection of the p-radial distribution on Bpn 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.

2010 AMS Mathematics Subject Classification: Primary 52A23; Secondary 60F10.

Keywords and phrases: large deviation principle, lpn-ball, random projection, Stiefel manifold.

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