• Corpus ID: 226976761

Geometric and functional inequalities for log-concave probability sequences

  title={Geometric and functional inequalities for log-concave probability sequences},
  author={Arnaud Marsiglietti and James Melbourne},
  journal={arXiv: Probability},
We investigate various geometric and functional inequalities for the class of log-concave probability sequences. We prove dilation inequalities for log-concave probability measures on the integers. A functional analog of this geometric inequality is derived, giving large and small deviation inequalities from a median, in terms of a modulus of regularity. Our methods are of independent interest, we find that log-affine sequences are the extreme points of the set of log-concave sequences… 

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