Entropic Measure on Multidimensional Spaces
| dc.creator | Sturm, Karl-Theodor | |
| dc.date | 2009-01-13 | |
| dc.date.accessioned | 2026-07-07T12:29:00Z | |
| dc.date.available | 2026-07-07T12:29:00Z | |
| dc.description | We construct the entropic measure $\mathbb{P}^β$ on compact manifolds of any dimension. It is defined as the push forward of the Dirichlet process (another random probability measure, well-known to exist on spaces of any dimension) under the {\em conjugation map} $$\Conj:\mathcal{P}(M)\to\mathcal{P}(M).$$ This conjugation map is a continuous involution. It can be regarded as the canonical extension to higher dimensional spaces of a map between probability measures on 1-dimensional spaces characterized by the fact that the distribution functions of $μ$ and $\Conj(μ)$ are inverse to each other. We also present an heuristic interpretation of the entropic measure as $$d\mathbb{P}^β(μ)=\frac{1}{Z}\exp(-β\cdot {Ent} (μ|m))\cdot d\mathbb{P}^0(μ).$$ | |
| dc.description | 17 pages, 6 figures | |
| dc.identifier | https://arxiv.org/abs/0901.1815 | |
| dc.identifier | http://arxiv.org/abs/0901.1815 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/215730 | |
| dc.subject | Probability | |
| dc.subject | 60G57; 28C20; 49N90; 49Q20; 58J65 | |
| dc.title | Entropic Measure on Multidimensional Spaces | |
| dc.type | text |