Details

Autor(en) / Beteiligte

• Madiman, Mokshay
• Melbourne, James
• Xu, Peng

Titel

Forward and Reverse Entropy Power Inequalities in Convex Geometry

Ist Teil von

• Convexity and Concentration, p.427-485

Ort / Verlag

New York, NY: Springer New York

Link zum Volltext

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• The entropy power inequality, which plays a fundamental role in information theory and probability, may be seen as an analogue of the Brunn-Minkowski inequality. Motivated by this connection to Convex Geometry, we survey various recent developments on forward and reverse entropy power inequalities not just for the Shannon-Boltzmann entropy but also more generally for Rényi entropy. In the process, we discuss connections between the so-called functional (or integral) and probabilistic (or entropic) analogues of some classical inequalities in geometric functional analysis.