On the analogue of the concavity of entropy power in the Brunn-Minkowski theory

2013/02/25 by Matthieu Fradelizi, Fradelizi, Matthieu, Arnaud Marsiglietti +1 · 1 citation
Computer Science · Mathematics · #52A40 #94A17 #FOS: Computer and information sciences #FOS: Mathematics #Functional Analysis (math.FA) #Information Theory (cs.IT) #Metric Geometry (math.MG) #cs.IT #math.FA #math.IT #math.MG #msc:52A40 #msc:94A17

paper · pdf · doi:10.48550/arxiv.1302.6093

arxiv created 2013/02/25 · arxiv updated 2013/02/26

Abstract

Elaborating on the similarity between the entropy power inequality and the Brunn-Minkowski inequality, Costa and Cover conjectured in \it On the similarity of the entropy power inequality and the Brunn-Minkowski inequality (IEEE Trans. Inform. Theory 30 (1984), no. 6, 837-839) the (1)/(n)-concavity of the outer parallel volume of measurable sets as an analogue of the concavity of entropy power. We investigate this conjecture and study its relationship with geometric inequalities.

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