Keywords
- Typical Sequence
- Positive Sequence
- Multivariate Case
- Independent Copy
- Real Random Variable
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Barthe F. (1999) Restricted Prékopa-Leindler inequality. Pacific J. Math. 189(2):211–222
Brascamp H.J., Lieb E.H., Luttinger J.M. (1974) A general rearrangement inequality for multiple integrals. J. Funct. Analysis 17:227–237
Cover, T.M., Thomas, J.A. (1991) Elements of information theory. Wiley Series in Telecommunications. John Wiley & Sons, Inc., New York.
Dembo A., Cover T.M., Thomas J.A. (1991) Information theoretic inequalities. IEEE Transactions on Information Theory 37(6):1501–1518
Lieb E.H. (1978) Proof of an entropy conjecture of Wehrl. Commun. Math. Phys. 62:35–41
Shannon C.E., Weaver W. (1963) The Mathematical Theory of Communications. University of Illinois Press
Stam A.J. (1959) Some inequalities satisfied by the quantities of information of Fisher and Shannon. Information and Control 2:101–112
Szarek S.J., Voiculescu D. (1996) Volumes of restricted Minkowski sums and the free analogue of the entropy power inequality. Commun. Math. Phys. 178:563–570
Voiculescu D. (1993) The analogues of entropy and of Fisher's information measure in free probability theory, I. Commun. Math. Phys. 155:71–92; (1994) ibidem, II. Invent. Math. 118:411–440; (1996) ibidem, III, The absence of Cartan subalgebras. Geom. Funct. Anal. 6(1):172–199; (1997) ibidem, IV, Maximum entropy and freeness. In: Free Probability Theory (Waterloo, ON, 1995), Fields Inst. Commun., 12, Amer. Math. Soc., 293–302; (1998) ibidem, V, Noncommutative Hilbert transforms. Invent. Math. 132(1):189–227
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer-Verlag
About this chapter
Cite this chapter
Szarek, S.J., Voiculescu, D. (2000). Shannon’s entropy power inequality via restricted minkowski sums. In: Milman, V.D., Schechtman, G. (eds) Geometric Aspects of Functional Analysis. Lecture Notes in Mathematics, vol 1745. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0107219
Download citation
DOI: https://doi.org/10.1007/BFb0107219
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-41070-6
Online ISBN: 978-3-540-45392-5
eBook Packages: Springer Book Archive
