Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8900469 | Advances in Applied Mathematics | 2018 | 35 Pages |
Abstract
The paper provides a description of the large deviation behavior for the Euclidean norm of projections of âpn-balls to high-dimensional random subspaces. More precisely, for each integer nâ¥1, let knâ{1,â¦,nâ1}, E(n) be a uniform random kn-dimensional subspace of Rn and X(n) be a random point that is uniformly distributed in the âpn-ball of Rn for some pâ[1,â]. Then the Euclidean norms âPE(n)X(n)â2 of the orthogonal projections are shown to satisfy a large deviation principle as the space dimension n tends to infinity. Its speed and rate function are identified, making thereby visible how they depend on p and the growth of the sequence of subspace dimensions kn. As a key tool we prove a probabilistic representation of âPE(n)X(n)â2 which allows us to separate the influence of the parameter p and the subspace dimension kn.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
David Alonso-Gutiérrez, Joscha Prochno, Christoph Thäle,