Subadditivity of the entropy and its relation to Brascamp-Lieb type inequalities
| dc.creator | Carlen, Eric A. | |
| dc.creator | Cordero-Erausquin, Dario | |
| dc.date | 2007-10-03 | |
| dc.date | 2008-01-29 | |
| dc.date.accessioned | 2026-07-07T08:56:39Z | |
| dc.date.available | 2026-07-07T08:56:39Z | |
| dc.description | We prove a general duality result showing that a Brascamp--Lieb type inequality is equivalent to an inequality expressing subadditivity of the entropy, with a complete correspondence of best constants and cases of equality. This open a new approach to the proof of Brascamp--Lieb type inequalities, via subadditivity of the entropy. We illustrate the utility of this approach by proving a general inequality expressing the subadditivity property of the entropy on $\R^n$, and fully determining the cases of equality. As a consequence of the duality mentioned above, we obtain a simple new proof of the classical Brascamp--Lieb inequality, and also a fully explicit determination of all of the cases of equality. We also deduce several other consequences of the general subadditivity inequality, including a generalization of Hadamard's inequality for determinants. Finally, we also prove a second duality theorem relating superadditivity of the Fisher information and a sharp convolution type inequality for the fundamental eigenvalues of Schrödinger operators. Though we focus mainly on the case of random variables in $\R^n$ in this paper, we discuss extensions to other settings as well. | |
| dc.description | This is the revised version taking into account points made by the referee | |
| dc.identifier | https://arxiv.org/abs/0710.0870 | |
| dc.identifier | http://arxiv.org/abs/0710.0870 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/146686 | |
| dc.subject | Functional Analysis | |
| dc.subject | Probability | |
| dc.subject | 26D15; 94A17 | |
| dc.title | Subadditivity of the entropy and its relation to Brascamp-Lieb type inequalities | |
| dc.type | text |