On the Subadditivity of the Entropy on the Sphere
Change log
Authors
Einav, A
Abstract
We present a refinement of a known entropic inequality on the sphere, finding
suitable conditions under which the uniform probability measure on the sphere
behaves asymptomatically like the Gaussian measure on
Description
Keywords
math.FA, math.FA, cs.IT, math-ph, math.IT, math.MP, 39B62, 52A40, 60D99, 82C40, 94A17
Journal Title
Journal of Geometric Analysis
Conference Name
Journal ISSN
1050-6926
1559-002X
1559-002X
Volume Title
Publisher
Springer Science and Business Media LLC
Publisher DOI
Sponsorship
Engineering and Physical Sciences Research Council (EP/L002302/1)
We would like to greatly thank Eric Carlen for many discussions and insights on key ideas all along the progression of this work, without which this paper would never have seen the light of day. We would also like to offer our gratitude to Nathael Gozlan for providing us with a reference for the “distorted” HWI inequality we use in Sect. 3, and Clément Mouhot for several discussions on the present results. The author was supported by EPSRC Grant EP/L002302/1.