Entropy and a generalisation of `Poincare's Observation'
| dc.creator | Johnson, Oliver | |
| dc.date | 2002-01-29 | |
| dc.date.accessioned | 2026-07-07T08:06:01Z | |
| dc.date.available | 2026-07-07T08:06:01Z | |
| dc.description | Consider a sphere of radius root(n) in n dimensions, and consider X, a random variable uniformly distributed on its surface. Poincare's Observation states that for large n, the distribution of the first k coordinates of X is close in total variation distance to the standard normal N(0,I_k). In this paper, we consider a larger family of manifolds, and X taking a more general distribution on the surfaces. We establish a bound in the stronger Kullback--Leibler sense of relative entropy, and discuss its sharpness, providing a necessary condition for convergence in this sense. We show how our results imply the equivalence of ensembles for a wider class of test functions than is standard. We also deduce results of de Finetti type, concerning a generalisation of the idea of orthogonal invariance. | |
| dc.description | 12 pages | |
| dc.identifier | https://arxiv.org/abs/math/0201273 | |
| dc.identifier | http://arxiv.org/abs/math/0201273 | |
| dc.identifier | Mathematical Proceedings of the Cambridge Philosophical Society, Vol 135/2, 2003, pages 375-384 | |
| dc.identifier | doi:10.1017/S0305004103006881 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/130464 | |
| dc.subject | Probability | |
| dc.subject | Statistics Theory | |
| dc.subject | 60F99, 62B10, 94A17 | |
| dc.title | Entropy and a generalisation of `Poincare's Observation' | |
| dc.type | text |