A Strengthened Entropy Power Inequality for Log-Concave Densities

  title={A Strengthened Entropy Power Inequality for Log-Concave Densities},
  author={Giuseppe Toscani},
  journal={IEEE Transactions on Information Theory},
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. 
Highly Cited
This paper has 24 citations. REVIEW CITATIONS

From This Paper

Topics from this paper.
17 Citations
36 References
Similar Papers


Publications citing this paper.
Showing 1-10 of 17 extracted citations


Publications referenced by this paper.
Showing 1-10 of 36 references

Speed of approach to equilibrium for Kac’s caricature of a Maxwellian gas

  • H. P. McKean
  • Arch. Rat. Mech. Anal. 21,
  • 1966
Highly Influential
8 Excerpts

Heat equation and convolution inequalities

  • G. Toscani
  • Milan J. Math. (in press)
  • 2014
2 Excerpts

Lyapunov functionals for the heat equation and sharp inequalities

  • G. Toscani
  • Atti Acc. Peloritana Pericolanti, Classe Sc. Fis…
  • 2013
1 Excerpt

Similar Papers

Loading similar papers…