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

Communications in Mathematical Physics

Volumn 178, Issue 3, 1996, Pages 563-570

  Szarek, Stanislaw J ^a   Voiculescu, Dan ^b  

^a CASE WESTERN RESERVE UNIVERSITY   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030551656     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02108815     Document Type: Article

References (11)

1. Blachman, N.M.: The convolution inequality for entropy powers. IEEE Trans. Inform. Theory 2, 267-327 (1965)
2. Brascamp, H.J., Lieb, E.H., Luttinger, J.M.: A general rearrangement inequality for multiple integrals. J. Funct. Anal. 17, 227-237 (1974)
3. Carlen, E.A.: Superadditivity of Fisher's information and logarithmic Sobolev inequalities. J. Funct. Anal. 101, 194-211 (1991)
4. Pisier, G.: The Volume of Convex Bodies and Banach Space Geometry. Cambridge: Cambridge Univ. Press, 1989
5. Schneider, R.: Convex bodies: The Brunn-Minkowski theory. Encyclopedia of Mathematics and Its Applications 44, Cambridge: Cambridge Univ. Press, 1993
6. Shannon, C.E., Weaver, W.: The Mathematical Theory of Communications. University of Illinois Press, 1963
7. Stam, A.J.: Some inequalities satisfied by the quantities of information of Fisher and Shannon. Information and Control 2, 101-112 (1959)
8. Voiculescu, D.: The analogues of entropy and of Fisher's information measure in free probability theory, I. Commun. Math. Phys. 155, 71-92 (1993);
9. ibidem II. Invent. Math. 118, 411-440 (1994);
10. ibidem III, IHES preprint, May 1995 (to appear in GAFA)
11. Voiculescu, D., Dykema, D., Nica, A.: Free Random Variables. CRM Monograph Series, Vol. 1, Providence, RI: American Mathematical Society, 1992