Free diffusions, free entropy and free Fisher information

Philippe Biane; Roland Speicher

Annales de l'I.H.P. Probabilités et statistiques (2001)

  • Volume: 37, Issue: 5, page 581-606
  • ISSN: 0246-0203

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Biane, Philippe, and Speicher, Roland. "Free diffusions, free entropy and free Fisher information." Annales de l'I.H.P. Probabilités et statistiques 37.5 (2001): 581-606. <http://eudml.org/doc/77700>.

@article{Biane2001,
author = {Biane, Philippe, Speicher, Roland},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {free diffusions; free entropy; free Fisher information},
language = {eng},
number = {5},
pages = {581-606},
publisher = {Elsevier},
title = {Free diffusions, free entropy and free Fisher information},
url = {http://eudml.org/doc/77700},
volume = {37},
year = {2001},
}

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
PB - Elsevier
VL - 37
IS - 5
SP - 581
EP - 606
LA - eng
KW - free diffusions; free entropy; free Fisher information
UR - http://eudml.org/doc/77700
ER -

References

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  1. [1] P Biane, Free brownian motion, free stochastic calculus and random matrices, in: Voiculescu D.V (Ed.), Free Probability Theory, Fields Institute Communications, 12, 1997, pp. 1-20. Zbl0873.60056MR1426833
  2. [2] P Biane, On the free convolution with a semi-circular distribution, Indiana University Math. J.46 (1997) 705-717. Zbl0904.46045MR1488333
  3. [3] P Biane, Free probability for probabilists, MSRI Preprint40 (1998). Zbl1105.46045MR2032363
  4. [4] P Biane, Processes with free increments, Math. Zeit.227 (1998) 143-174. Zbl0902.60060MR1605393
  5. [5] P Biane, R Speicher, Stochastic calculus with respect to free brownian motion and analysis on Wigner space, Probab. Theory Related Fields112 (1998) 373-409. Zbl0919.60056MR1660906
  6. [6] M Douglas, Stochastic master fields, Phys. Lett. B344 (1995) 117-126. MR1314776
  7. [7] M Douglas, Large N quantum field theory and matrix models, in: Voiculescu D.V (Ed.), Free Probability Theory, Fields Institute Communications, 12, 1997, pp. 21-40. Zbl0871.46035MR1426834
  8. [8] F.J Dyson, A brownian motion model for the eigenvalues of a random matrix, J. Math. Phys.3 (1962) 1191-1198. Zbl0111.32703MR148397
  9. [9] M.I Freidlin, A.D Wentzell, Random Perturbations of Dynamical Systems, Grundlehren der Mathematischen Wissenschaften, 260, Springer-Verlag, New York, 1998. Zbl0522.60055MR1652127
  10. [10] M Fukushima, Y Oshima, M Takeda, Dirichlet Forms and Symmetric Markov Processes, de Gruyter Studies in Mathematics, 19, Walter de Gruyter, Berlin, 1994. Zbl0838.31001MR1303354
  11. [11] R Gopakumar, D.J Gross, Mastering the master field, Nucl. Phys. B451 (1995) 379-415. Zbl0925.46024MR1352420
  12. [12] J Greensite, M.B Halpern, Quenched master fields, Nucl. Phys.211 (1988) 343-368. 
  13. [13] V.V Peller, Hankel operators in the perturbation theory of unitary and self-adjoint operators, Funct. Anal. Appl.19 (1985) 111-123. Zbl0587.47016MR800919
  14. [14] R Speicher, 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. Zbl0935.46056MR1407898
  15. [15] D.W Stroock, Logarithmic Sobolev inequalities for Gibbs states, in: Dell'Antonio G, Mosco U (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. Zbl0801.60056MR1292280
  16. [16] E.B Saff, V Totik, Logarithmic Potentials with External Fields, Grundlehren der Mathematischen Wissenschaften, 316, Springer-Verlag, Berlin, 1997. Zbl0881.31001MR1485778
  17. [17] D.V Voiculescu, Limit laws for random matrices and free products, Invent. Math.104 (1991) 201-220. Zbl0736.60007MR1094052
  18. [18] D.V Voiculescu, The analogues of entropy and of Fisher's information measure in free probability theory. I, Comm. Math. Phys.155 (1993) 71-92. Zbl0781.60006MR1228526
  19. [19] D.V Voiculescu, The derivative of order 1/2 of a free convolution by a free semi-circular distribution, Indiana University Math. J.46 (1997) 697-703. Zbl0920.46046MR1488332
  20. [20] D.V Voiculescu, Lectures on Free Probability Theory, Saint Flour Summer School, Lecture Notes in Mathematics, Springer, Berlin, 1999. Zbl1015.46037
  21. [21] D.V Voiculescu, The analogues of entropy and of Fisher's information measure in free probability theory. V: noncommutative Hilbert transform, Invent. Math.132 (1998) 189-227. Zbl0930.46053MR1618636
  22. [22] D.V Voiculescu, K Dykema, A Nica, Free Random Variables, CRM Monograph Series No. 1, Amer. Math. Soc, Providence, RI, 1992. Zbl0795.46049MR1217253

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