Entropic Measure on Multidimensional Spaces

Details Entropic Measure on Multidimensional Spaces Entropic Measure on Multidimensional Spaces

2009-01-13

arxiv.org/abs/0901.1815v1

Mathematics

Probability

17 pages, 6 figures

Scientific paper

We construct the entropic measure $\mathbb{P}^\beta$ 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 $\mu$ and $\Conj(\mu)$ are inverse to each other. We also present an heuristic interpretation of the entropic measure as $$d\mathbb{P}^\beta(\mu)=\frac{1}{Z}\exp(-\beta\cdot {Ent} (\mu|m))\cdot d\mathbb{P}^0(\mu).$$

Affiliated with

Also associated with

No associations

Rating

Entropic Measure on Multidimensional Spaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Entropic Measure on Multidimensional Spaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Entropic Measure on Multidimensional Spaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-72298