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arXiv · 1507.07711

Self-similar solutions of R\'enyi's entropy and the concavity of its entropy power

Agapitos N. Hatzinikitas
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Abstract

We study the class of self-similar probability density functions with finite mean and variance which maximize R\'{e}nyi's entropy. The investigation is restricted in the Schwartz space $S(\mathbb{R}^d)$ and in the space of $l$-differentiable compactly supported functions $C_c^l(\mathbb{R}^d)$. Interestingly the solutions of this optimization problem do not coincide with the solutions of the usual porous medium equation with a Dirac point source, as it occurs in the optimization of Shannon's entropy. We also study the concavity of the entropy power in $\mathbb{R}^d$ with respect to time using two different methods. The first one takes advantage of the solutions determined earlier while the second one is based on a setting that could be used for Riemannian manifolds.

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Agapitos N. Hatzinikitas. 2015-07-28. Self-similar solutions of R\'enyi's entropy and the concavity of its entropy power. https://doi.org/10.3390/e17096056

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