A Strengthened Entropy Power Inequality for Log-Concave Densities

@article{Toscani2015ASE,
  title={A Strengthened Entropy Power Inequality for Log-Concave Densities},
  author={Giuseppe Toscani},
  journal={IEEE Transactions on Information Theory},
  year={2015},
  volume={61},
  pages={6550-6559}
}
We show that Shannon's entropy-power inequality admits a strengthened version in the case in which the densities are log-concave. In such a case, in fact, one can extend the Blachman-Stam argument to obtain a sharp inequality for the second derivative of Shannon's entropy functional with respect to the heat semigroup. 
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