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.
