Free Entropy
By D. Voiculescu. 2001
93 citations recorded by the source corpus.
Free entropy is the analogue of entropy in free probability theory. The paper is a survey of free entropy, its applications to von Neumann algebras and its connections to random matrix theory, as well as a discussion of open problems and of a basic variational problem, connected to random multimatrix models.
Subfields: Computational Theory and Mathematics, Mathematical Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/275609ffbc88412be3d4c48a5cb335e35d8facf4
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In Computational Theory and Mathematics
- Roland Vergnioux
- Édouard Maurel-Segala
- Yoann Dabrowski
- Alain Connes
- Mylène Maïda
- Benoît Collins
- Michael Brannan
- D. Shlyakhtenko
In Mathematical Physics
- Michael Brannan
- Yoann Dabrowski
- Édouard Maurel-Segala
- Benoît Collins
- Roland Vergnioux
- Alain Connes
- Mylène Maïda
- D. Shlyakhtenko
In Statistical and Nonlinear Physics
- Roland Vergnioux
- Édouard Maurel-Segala
- Yoann Dabrowski
- Alain Connes
- Mylène Maïda
- Benoît Collins
- Michael Brannan
- D. Shlyakhtenko
Citations in the corpus
- Circular law theorem for random Markov matrices (2008, unknown): “is up to a sign the Voiculescu free entropy of μ in free probability theory [44].”
- Free transport-entropy inequalities for non-convex potentials and application to concentration for random matrices (2012, methodology): “ion. Therefore it is natural to ask whether the semi-circle law satisfies a free analogue of the transport-entropy inequality T2,with the entropy replaced by the free entropy defined by Voiculescu (see [Voi02] for a quick review). A positive answer to this question was given by Biane and Voiculescu in”
- The Connes embedding property for quantum group von Neumann algebras (2014, methodology): “on. In this section we present an application of our hyperlinearity results to the computation of the free entropy dimension of the canonical generators of L∞(O+ N). We refer the reader to the survey [41] for details on the various notions of free entropy dimension and related concepts. Let Γ be a fi”
- A free stochastic partial differential equation (2010, methodology): “For more details, we refer the reader to the survey [45] for a list of properties as well as applications of free entropies in the theory of von Neumann algebras.”
- L 2-homology for von Neumann algebras (2003, background): “We have completely unexpectedly found a connection between our definition, involving algebraic homology, and the theory of free entropy dimension developed by Voiculescu and his followers ([Voi93, Voi94, Voi96, Voi98], see also [Voi02] and references therein).”