Volumes of restricted Minkowski sums and the free analogue of the entropy power inequality

DOI10.1007/BF02108815zbMath0863.46042arXivmath/9510203MaRDI QIDQ1924035

Stanislaw J. Szarek, Dan-Virgil Voiculescu

Publication date: 13 October 1996

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9510203

zbMATH Keywords

entropyfree probability theoryfree productsBrunn-Minkowski inequalitynoncommutative probability theoryShannon's entropy power inequalityvolumes of matricial microstates

Mathematics Subject Classification ID

Free probability and free operator algebras (46L54) Noncommutative probability and statistics (46L53) Noncommutative measure and integration (46L51) Foundations of probability theory (60A99)

Related Items (11)

The Brunn-Minkowski inequality ⋮ The entropy power inequality with quantum conditioning ⋮ A free analogue of Shannon's problem on monotonicity of entropy ⋮ Brunn-Minkowski and Zhang inequalities for convolution bodies ⋮ Reverse Brunn-Minkowski and reverse entropy power inequalities for convex measures ⋮ A discrete complement of Lyapunov's inequality and its information theoretic consequences ⋮ REMARKS ON A SEMICIRCULAR PERTURBATION OF THE FREE FISHER INFORMATION ⋮ Autour de l'inégalité de Brunn-Minkowski ⋮ The conditional entropy power inequality for Gaussian quantum states ⋮ A (one-dimensional) free Brunn-Minkowski inequality ⋮ Discussions around Voiculescu's free entropies.

Cites Work

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• Superadditivity of Fisher's information and logarithmic Sobolev inequalities
• The analogues of entropy and of Fisher's information measure in free probability theory. I
• A general rearrangement inequality for multiple integrals
• Free Random Variables
• Some inequalities satisfied by the quantities of information of Fisher and Shannon
• The convolution inequality for entropy powers

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