The analogues of entropy and of Fisher's information measure in free probability theory VI. Liberation and mutual free information

Advances in Mathematics

Volumn 146, Issue 2, 1999, Pages 101-166

  Voiculescu, Dan ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

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[No Author keywords available]

Indexed keywords

EID: 0033604007     PISSN: 00018708     EISSN: None     Source Type: Journal    
DOI: 10.1006/aima.1998.1819     Document Type: Article

References (17)

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11. 11. D. Voiculescu, The analogues of entropy and of Fisher's information measure in free probability theory, Commun. Math. Phys. 155 (1993), 71-92; ibid. II: Invent. Math. 118 (1994), 411-440; ibid. III: The absence of Cartan subalgebras, Geom. Funct. Anal. 6, No. 1 (1996), 172-199; ibid. IV: Maximum entropy and freeness, in "Free Probability Theory" (D. Voiculescu, Ed.), pp. 293-302, Fields Institute Communications, Vol. 12, Am. Math. Soc., Providence, RI, (1997); ibid. V: Noncommutative Hilbert transforms, Invent. Math. 132 (1998), 182-227.
12. 11. D. Voiculescu, The analogues of entropy and of Fisher's information measure in free probability theory, Commun. Math. Phys. 155 (1993), 71-92; ibid. II: Invent. Math. 118 (1994), 411-440; ibid. III: The absence of Cartan subalgebras, Geom. Funct. Anal. 6, No. 1 (1996), 172-199; ibid. IV: Maximum entropy and freeness, in "Free Probability Theory" (D. Voiculescu, Ed.), pp. 293-302, Fields Institute Communications, Vol. 12, Am. Math. Soc., Providence, RI, (1997); ibid. V: Noncommutative Hilbert transforms, Invent. Math. 132 (1998), 182-227.
13. 11. D. Voiculescu, The analogues of entropy and of Fisher's information measure in free probability theory, Commun. Math. Phys. 155 (1993), 71-92; ibid. II: Invent. Math. 118 (1994), 411-440; ibid. III: The absence of Cartan subalgebras, Geom. Funct. Anal. 6, No. 1 (1996), 172-199; ibid. IV: Maximum entropy and freeness, in "Free Probability Theory" (D. Voiculescu, Ed.), pp. 293-302, Fields Institute Communications, Vol. 12, Am. Math. Soc., Providence, RI, (1997); ibid. V: Noncommutative Hilbert transforms, Invent. Math. 132 (1998), 182-227.
14. 11. D. Voiculescu, The analogues of entropy and of Fisher's information measure in free probability theory, Commun. Math. Phys. 155 (1993), 71-92; ibid. II: Invent. Math. 118 (1994), 411-440; ibid. III: The absence of Cartan subalgebras, Geom. Funct. Anal. 6, No. 1 (1996), 172-199; ibid. IV: Maximum entropy and freeness, in "Free Probability Theory" (D. Voiculescu, Ed.), pp. 293-302, Fields Institute Communications, Vol. 12, Am. Math. Soc., Providence, RI, (1997); ibid. V: Noncommutative Hilbert transforms, Invent. Math. 132 (1998), 182-227.
15. 11. D. Voiculescu, The analogues of entropy and of Fisher's information measure in free probability theory, Commun. Math. Phys. 155 (1993), 71-92; ibid. II: Invent. Math. 118 (1994), 411-440; ibid. III: The absence of Cartan subalgebras, Geom. Funct. Anal. 6, No. 1 (1996), 172-199; ibid. IV: Maximum entropy and freeness, in "Free Probability Theory" (D. Voiculescu, Ed.), pp. 293-302, Fields Institute Communications, Vol. 12, Am. Math. Soc., Providence, RI, (1997); ibid. V: Noncommutative Hilbert transforms, Invent. Math. 132 (1998), 182-227.
16. 12. D. Voiculescu, A note on free Markovianity, in preparation.
17. 13. D. Voiculescu, K. J. Dykema, and A. M. Nica, "Free Random Variables," CRM Monograph Series, Vol. 1, Am. Math. Soc., Providence, RI, 1992.