Some Minimization Problems for the Free Analogue of the Fisher Information

Alexandru Nica, Dimitri Shlyakhtenko, Roland Speicher

Type: Article

Publication Date: 1999-02-01

Citations: 24

DOI: https://doi.org/10.1006/aima.1998.1780

View Publication

Locations

Advances in Mathematics - View
arXiv (Cornell University) - View - PDF

Similar Works

Action	Title	Year	Authors
+	Some minimization problems for the free analogue of the Fisher information	1998	Alexandru Nica Dimitri Shlyakhtenko Roland Speicher
+	Maximality of the microstates free entropy for R-diagonal elements	1998	Alexandru Nica Dimitri Shlyakhtenko Roland Speicher
+	Rectangular random matrices, related free entropy and free Fisher's information	2005	Florent Benaych-Georges
+ PDF Chat	Maximality of the microstates free entropy for R-diagonal elements	1999	Alexandru Nica Dimitri Shlyakhtenko Roland Speicher
+	A Microstates Approach to Relative Free Entropy	1998	Dimitri Shlyakhtenko
+	Free Entropy χ ∗: The Non-microstates Approach via Free Fisher Information	2017	James A. Mingo Roland Speicher
+ PDF Chat	ORBITAL APPROACH TO MICROSTATE FREE ENTROPY	2009	Fumio Hiai Takuho Miyamoto Yoshimichi Ueda
+	Free fisher information and amalgamated freeness	2004	Bin Meng Maozheng Guo Xiaohong Cao
+	Free Entropy	2002	Dan Voiculescu
+	Free entropy of noncommutative random variables	2006	Fumio Hiai Dénes Petz
+ PDF Chat	COLLECTIVE POTENTIAL FOR LARGE-N HAMILTONIAN MATRIX MODELS AND FREE FISHER INFORMATION	2003	Abhishek Agarwal Levent Akant Govind S. Krishnaswami S. G. Rajeev
+ PDF Chat	A MICROSTATES APPROACH TO RELATIVE FREE ENTROPY	2002	Dimitri Shlyakhtenko
+	Absence of algebraic relations and of zero divisors under the assumption of finite non-microstates free Fisher information	2014	Tobias Mai Roland Speicher Moritz Weber
+	Free Random Matrices	2020	Marc Potters Jean‐Philippe Bouchaud
+	A construction which relates c-freeness to infinitesimal freeness	2019	Maxime Février Mitja Mastnak Alexandru Nica Kamil Szpojankowski
+	A construction which relates c-freeness to infinitesimal freeness	2018	Maxime Février Mitja Mastnak Alexandru Nica Kamil Szpojankowski
+	A construction which relates c-freeness to infinitesimal freeness	2018	Maxime Février Mitja Mastnak Alexandru Nica Kamil Szpojankowski
+	Lecture Notes on "Free Probability Theory"	2019	Roland Speicher
+	R-Transforms of Free Joint Distributions and Non-crossing Partitions	1996	Alexandru Nica
+	Aspects of free analysis	2008	Dan-Virgil Voiculescu

Works That Cite This (21)

Action	Title	Year	Authors
+	Operator-valued distributions: I. Characterizations of freeness	2002	Alexandru Nica Dimitri Shlyakhtenko Roland Speicher
+ PDF Chat	Rectangular random matrices, related convolution	2008	Florent Benaych-Georges
+ PDF Chat	Operator-valued free Fisher information of random matrices	2010	Bin Meng
+	Some applications of free Fisher information on frame theory	2005	Bin Meng Maozheng Guo Xiaohong Cao
+	R-Cyclic Families of Matrices in Free Probability	2002	Alexandru Nica Dimitri Shlyakhtenko Roland Speicher
+	Maximality of the microstates free entropy for R-diagonal elements	1998	Alexandru Nica Dimitri Shlyakhtenko Roland Speicher
+ PDF Chat	On the powers of Voiculescu's circular element	2001	Ferenc Oravecz
+	Free entropy	2000	Dan Voiculescu
+ PDF Chat	Entropy considerations in the noncommutative setting	2000	Patricia Giurgescu
+	None	2002	Alexandru Nica Dimitri Shlyakhtenko Roland Speicher

Works Cited by This (6)

Action	Title	Year	Authors
+	$R$-diagonal pairs - a common approach to Haar unitaries and circular elements	1996	Alexandru Nica Roland Speicher
+	The analogues of entropy and of Fisher's information measure in free probability theory, II	1994	Dan Voiculescu
+	The analogues of entropy and of fisher's information measure in free probability theory III: The absence of cartan subalgebras	1996	Dan Voiculescu
+	Free entropy with respect to a completely positive map	2000	Dimitri Shlyakhtenko
+	Free Random Variables	1992	Dan Voiculescu Kenneth J. Dykema Alexandru Nica
+ PDF Chat	The analogues of entropy and of Fisher's information measure in free probability theory, I	1993	Dan Voiculescu