Entropie libre et algèbres d'opérateurs
Séminaire Bourbaki : volume 2000/2001, exposés 880-893, Astérisque, no. 282 (2002), Talk no. 889, 22 p. 
@incollection{SB_2000-2001__43__279_0,
     author = {Biane, Philippe},
     title = {Entropie libre et alg\`ebres d'op\'erateurs},
     booktitle = {S\'eminaire Bourbaki : volume 2000/2001, expos\'es 880-893},
     author = {Collectif},
     series = {Ast\'erisque},
     note = {talk:889},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {282},
     year = {2002},
     zbl = {1032.46076},
     mrnumber = {1975182},
     language = {fr},
     url = {http://www.numdam.org/item/SB_2000-2001__43__279_0/}
}
TY  - CHAP
AU  - Biane, Philippe
TI  - Entropie libre et algèbres d'opérateurs
BT  - Séminaire Bourbaki : volume 2000/2001, exposés 880-893
AU  - Collectif
T3  - Astérisque
N1  - talk:889
PY  - 2002
IS  - 282
PB  - Société mathématique de France
UR  - http://www.numdam.org/item/SB_2000-2001__43__279_0/
LA  - fr
ID  - SB_2000-2001__43__279_0
ER  - 
%0 Book Section
%A Biane, Philippe
%T Entropie libre et algèbres d'opérateurs
%B Séminaire Bourbaki : volume 2000/2001, exposés 880-893
%A Collectif
%S Astérisque
%Z talk:889
%D 2002
%N 282
%I Société mathématique de France
%U http://www.numdam.org/item/SB_2000-2001__43__279_0/
%G fr
%F SB_2000-2001__43__279_0
Biane, Philippe. Entropie libre et algèbres d'opérateurs, in Séminaire Bourbaki : volume 2000/2001, exposés 880-893, Astérisque, no. 282 (2002), Talk no. 889, 22 p. http://www.numdam.org/item/SB_2000-2001__43__279_0/

[BG] G. Ben Arous, A. Guionnet - Large deviations for Wigner's law and Voiculescu's non-commutative entropy. Probab. Theory Related Fields 108, no. 4 : 517-542, 1997. | MR | Zbl

[BS] P. Biane, R. Speicher - Free diffusions, free entropy and free Fisher information. Ann. Inst. H. Poincaré, Prob. Stat., 37 no. 5, 581-606, 2001. | Numdam | MR | Zbl

[BV] P. Biane, D. Voiculescu - A free probability analogue of the Wasserstein metric on the trace-state space. Geom. and Funct. Anal., 11 :1125-1138, 2001. | MR | Zbl

[C1] A. Connes - Classification of injective factors. Ann. Math. 104 : 73-115, 1976. | MR | Zbl

[C2] A. Connes - A factor of type II1 with countable fundamental group. J. Op. Theory 4 : 151-153, 1980. | MR | Zbl

[C3] A. Connes - Classification des facteurs. Proc. Symp. Pure Math. Operator algebras and applications, Vol 38, Part 2 :43-110, 1982. | MR | Zbl

[CDG] T. Cabanal-Duvillard, A. Guionnet - Large deviations upper bounds and non commutative entropies for some matrices ensembles. Ann. Prob, à paraître. | Zbl

[Di] J. Dixmier - Les algèbres d'opérateurs dans l'espace Hilbertien. 2ème édition, Gauthier-Villars, Paris, 1969. | MR | Zbl

[Dy1] K. J. Dykema - Free products of hyperfinite von Neumann algebras and free dimension. Duke Math. J. 69 no. 1 : 97-119, 1993. | MR | Zbl

[Dy2] K. J. Dykema - Two applications of free entropy. Math. Ann. 308, no. 3 : 547-558, 1997. | MR | Zbl

[DS] J. D. Deuschel, D. W. Stroock - Large deviations. Pure and Applied Mathematics, 137, Academic Press, Inc., Boston, MA, 1989. | MR | Zbl

[DZ] A. Dembo, O. Zeitouni - Large deviations techniques and applications. Second edition. Applications of Mathematics, 38, Springer-Verlag, New York, 1998. | MR | Zbl

[FM] J. Feldman, C. C. Moore - Ergodic equivalence relations, cohomology, and von Neumann algebras. II. Trans. Amer. Math. Soc. 234, no. 2 : 325-359, 1977. | MR | Zbl

[Ga] D. Gaboriau - Coût des relations d'équivalence et des groupes. Invent. Math. 139, no. 1 : 41-98,2000. | MR | Zbl

[Gl] Liming Ge - Applications of free entropy to finite von Neumann algebras I. Amer. J. Math. 119 :467-485, 1997. | MR | Zbl

[G2] Liming Ge - Applications of free entropy to finite von Neumann algebras II. Ann. Math. 147 :143-157,1998. | MR | Zbl

[GN] V. Ya. Golodets, N. I. Nessonov - T-property and nonisomorphic full factors of types II and III. J. Funct. Anal. 70 no. 1 : 80-89, 1987. | MR | Zbl

[GS] Liming Ge, Junhao Shen - Free entropy and property T factors. Proc. Nat. Acad. Sc. 97 no. 18 : 9881-9885, 2000. | MR | Zbl

[McD] D. Mc Duff - Uncountably many II1 factors, Ann. Math. 90 :372-378,1969. | MR | Zbl

[Me] M. L. Mehta - Random matrices. Second edition. Academic Press, Inc., Boston, MA, 1991. | MR | Zbl

[MvN] F. J. Murray, J. Von Neumann - On rings of operators IV. Ann. Math. 44 :716-708, 1943. | MR | Zbl

[vN1] J. Von Neumann - On rings of operators III. Ann. Math. 41 :94-161,1940. | Zbl

[vN2] J. Von Neumann - On rings of operators. Reduction theory. Ann. Math. 50 :401-485, 1949. | MR | Zbl

[NSS1] A. Nica, D. Shlyakhtenko, R. Speicher - Maximality of the microstates free entropy for R-diagonal elements. Pacific J. Math. 187 no. 2, 333-347, 1999. | MR | Zbl

[NSS2] A. Nica, D. Shlyakhtenko, R. Speicher - Some minimization problems for the free analogue of the Fisher information. Adv. Math. 141 no. 2, 282- 321, 1999. | MR | Zbl

[P] S. Popa - Orthogonal pairs of *-subalgebras in finite von Neumann algebras. J. Operator theory 9, 253-268, 1983. | MR | Zbl

[PV] L. Pastur, V. Vasilchuk - On the law of addition of random matrices. Comm. Math. Phys. 214 : 249-286, 2000. | MR | Zbl

[R] F. Rădulescu - Random matrices, amalgamated free products and subfactors of the von Neumann algebra of a free group, of noninteger index. Invent. Math. 115 no. 2, 347-389, 1994. | MR | Zbl

[Sh1] D. Shlyakhtenko - Prime type III factors. Proc. Nat. Acad. Sc. 97 no. 23 : 12439-12441,2000. | MR | Zbl

[Sh2] D. Shlyakhtenko - Microstates free entropy and cost of equivalence relations. math.OA/9912224.

[Sh3] D. Shlyakhtenko - Free entropy with respect to a completely positive map. Amer. J. Math. 122 no. 1, 45-81, 2000. | MR | Zbl

[Sk] G. Skandalis - Algèbres de von Neumann de groupes libres et probabilités non commutatives (d'après Voiculescu, etc.). Séminaire Bourbaki, Exp. n° 764, Vol. 1992/93. Astérisque No. 216 (1993), 87-102. | Numdam | MR | Zbl

[Sp1] R. Speicher - Combinatorial theory of the free product with amalgamation and operator-valued free probability theory. Mem. Amer. Math. Soc. 132 (1998), no. 627. | MR | Zbl

[Sp2] R. Speicher - Free probability theory and non-crossing partitions. Sém. Lothar. Combin. 39 (1997), Art. B39c, 38 pp. http://www.mat.univie.ac.at/slc/ | MR | Zbl

[St1] M. Ştefan - The primality of subfactors of finite index in the interpolated free group factors. Proc. Amer. Math. Soc. 126 no. 8 : 2299-2307, 1998. | MR | Zbl

[St2] M. Ştefan - The indecomposability of free group factors over nonprime sub-factors and abelian subalgebras. Preprint, 1999.

[Sz] S. Szarek - Nets of Grassmann manifold and orthogonal group. Proceedings of Research Workshop on Banach space Theory, Iowa Coty, Iowa : 169-185, 1981. | MR | Zbl

[VI] D. Voiculescu - Symmetries of some reduced free product C*-algebras. Operator algebras and their connections with topology and ergodic theory (Buşteni, 1983), Lecture Notes in Math., 1132 : 556-588, Springer, Berlin-New York, 1985. | MR | Zbl

[V2] D. Voiculescu - Limit laws for random matrices and free products. Inv. Math. 104 :201-220, 1983. | MR | Zbl

[V3] D. Voiculescu - The analogue of entropy and of Fisher's information theory in free probability theory II. Inv. Math. 118 :411-440, 1994. | MR | Zbl

[V4] D. Voiculescu - The analogue of entropy and of Fisher's information theory in free probability theory III : the absence of Cartan subalgebra. Geom. And Funct. Anal. Vol 6 No 1 :411-440, 1996. | MR | Zbl

[V5] D. Voiculescu - The analogue of entropy and of Fisher's information theory in free probability theory IV : maximum entropy and freeness. in Free probability, D. Voiculescu, ed., Fields Inst. Communications, Vol 12 :293-302, AMS Providence, 1997. | MR | Zbl

[V6] D. Voiculescu - The analogue of entropy and of Fisher's information theory in free probability theory V : non commutative Hilbert transform. Inv. Math. 132 :182-227, 1998. | MR | Zbl

[V7] D. Voiculescu - A strengthened asymptotic freeness result for random matrices with applications to free entropy. Internat. Math. Res. Notices no. 1, 41-63,1998. | MR | Zbl

[V8] D. Voiculescv - Free entropy dimension ≤ 1 for some generators of property T factors of type II1. J. Reine Angew. Math. 514 113-118, 1999. | Zbl