@article{AIHPB_2001__37_5_581_0, author = {Biane, Philippe and Speicher, Roland}, title = {Free diffusions, free entropy and free {Fisher} information}, journal = {Annales de l'I.H.P. Probabilit\'es et statistiques}, pages = {581--606}, publisher = {Elsevier}, volume = {37}, number = {5}, year = {2001}, mrnumber = {1851716}, zbl = {1020.46018}, language = {en}, url = {http://www.numdam.org/item/AIHPB_2001__37_5_581_0/} }
TY - JOUR AU - Biane, Philippe AU - Speicher, Roland TI - Free diffusions, free entropy and free Fisher information JO - Annales de l'I.H.P. Probabilités et statistiques PY - 2001 SP - 581 EP - 606 VL - 37 IS - 5 PB - Elsevier UR - http://www.numdam.org/item/AIHPB_2001__37_5_581_0/ LA - en ID - AIHPB_2001__37_5_581_0 ER -
Biane, Philippe; Speicher, Roland. Free diffusions, free entropy and free Fisher information. Annales de l'I.H.P. Probabilités et statistiques, Tome 37 (2001) no. 5, pp. 581-606. http://www.numdam.org/item/AIHPB_2001__37_5_581_0/
[1] Free brownian motion, free stochastic calculus and random matrices, in: (Ed.), Free Probability Theory, Fields Institute Communications, 12, 1997, pp. 1-20. | MR | Zbl
,[2] On the free convolution with a semi-circular distribution, Indiana University Math. J. 46 (1997) 705-717. | MR | Zbl
,[3] Free probability for probabilists, MSRI Preprint 40 (1998). | MR
,[4] Processes with free increments, Math. Zeit. 227 (1998) 143-174. | MR | Zbl
,[5] Stochastic calculus with respect to free brownian motion and analysis on Wigner space, Probab. Theory Related Fields 112 (1998) 373-409. | MR | Zbl
, ,[6] Stochastic master fields, Phys. Lett. B 344 (1995) 117-126. | MR
,[7] Large N quantum field theory and matrix models, in: (Ed.), Free Probability Theory, Fields Institute Communications, 12, 1997, pp. 21-40. | MR | Zbl
,[8] A brownian motion model for the eigenvalues of a random matrix, J. Math. Phys. 3 (1962) 1191-1198. | MR | Zbl
,[9] Random Perturbations of Dynamical Systems, Grundlehren der Mathematischen Wissenschaften, 260, Springer-Verlag, New York, 1998. | MR | Zbl
, ,[10] Dirichlet Forms and Symmetric Markov Processes, de Gruyter Studies in Mathematics, 19, Walter de Gruyter, Berlin, 1994. | MR | Zbl
, , ,[11] Mastering the master field, Nucl. Phys. B 451 (1995) 379-415. | MR | Zbl
, ,[12] Quenched master fields, Nucl. Phys. 211 (1988) 343-368.
, ,[13] Hankel operators in the perturbation theory of unitary and self-adjoint operators, Funct. Anal. Appl. 19 (1985) 111-123. | MR | Zbl
,[14] Combinatorial Theory of the Free Product with Amalgamation and Operator-Valued Free Probability Theory, Mem. Amer. Math. Soc., 627, Amer. Math. Soc, Providence, RI, 1998. | MR | Zbl
,[15] Logarithmic Sobolev inequalities for Gibbs states, in: , (Eds.), Dirichlet Forms, Lectures given at the First C.I.M.E., Session held in Varenna, June 8-19, Lecture Notes in Mathematics, 1563, Springer-Verlag, Berlin, 1993, pp. 194-228. | MR | Zbl
,[16] Logarithmic Potentials with External Fields, Grundlehren der Mathematischen Wissenschaften, 316, Springer-Verlag, Berlin, 1997. | MR | Zbl
, ,[17] Limit laws for random matrices and free products, Invent. Math. 104 (1991) 201-220. | MR | Zbl
,[18] The analogues of entropy and of Fisher's information measure in free probability theory. I, Comm. Math. Phys. 155 (1993) 71-92. | MR | Zbl
,[19] The derivative of order 1/2 of a free convolution by a free semi-circular distribution, Indiana University Math. J. 46 (1997) 697-703. | MR | Zbl
,[20] Lectures on Free Probability Theory, Saint Flour Summer School, Lecture Notes in Mathematics, Springer, Berlin, 1999. | Zbl
,[21] The analogues of entropy and of Fisher's information measure in free probability theory. V: noncommutative Hilbert transform, Invent. Math. 132 (1998) 189-227. | MR | Zbl
,[22] Free Random Variables, CRM Monograph Series No. 1, Amer. Math. Soc, Providence, RI, 1992. | MR | Zbl
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