Representations of Lie groups and random matrices

Transactions of the American Mathematical Society

Volumn 361, Issue 6, 2009, Pages 3269-3287

  Collins, Benoît ^a,b   Śniady, Piotr ^c  

^a UNIVERSITY OF OTTAWA   (Canada)

^b UNIVERSITÉ LYON 1   (France)

^c UNIVERSITY OF WROC AW   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77950548102     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9947-09-04624-8     Document Type: Article

References (23)

1. Philippe Biane. Representations of unitary groups and free convolution. Publ. Res. Inst. Math. Sci., 31 (1) : 63-79, 1995. MR1317523 (96c:22021)
2. Philippe Biane. Representations of symmetric groups and free probability. Adv. Math., 138 (1) : 126-181, 1998. MR1644993 (2001b:05225) (Pubitemid 128370263)
3. Theodor Bröcker and Tammo tom Dieck. Representations of compact Lie groups, volume 98 of Graduate Texts in Mathematics. Springer-Verlag, New York, 1995. MR1410059 (97i:22005)
4. Benoît Collins and Piotr Śniady. Representations of Lie groups, random matrices and free probability. In preparation, 2008.
5. Anatolij Dvurečenskij, Pekka Lahti, and Kari Ylinen. The uniqueness question in the multidimensional moment problem with applications to phase space observables. Rep. Math. Phys., 50 (1) : 55-68, 2002. MR1939941 (2003j:44010) (Pubitemid 36462051)
6. William Fulton and Joe Harris. Representation theory, volume 129 of Graduate Texts in Mathematics. Springer-Verlag, New York, 1991. MR1153249 (93a:20069)
7. N. Giri and W. von Waldenfels. An algebraic version of the central limit theorem. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 42 (2) : 129-134, 1978. MR0467880 (57:7731a)
8. Roe Goodman and Nolan R. Wallach. Representations and invariants of the classical groups, volume 68 of Encyclopedia of Mathematics and its Applications. Cambridge University Press, Cambridge, 1998. MR1606831 (99b:20073)
9. G. J. Heckman. Projections of orbits and asymptotic behavior of multiplicities for compact connected Lie groups. Invent. Math., 67 (2) : 333-356, 1982. MR665160 (84d:22019)
10. Kurt Johansson. Discrete orthogonal polynomial ensembles and the Plancherel measure. Ann. of Math. (2), 153 (1) : 259-296, 2001. MR1826414 (2002g:05188) (Pubitemid 33275952)
11. Anthony W. Knapp. Lie groups beyond an introduction, volume 140 of Progress in Mathematics. Birkhäuser Boston Inc., Boston, MA, second edition, 2002. MR1920389 (2003c:22001)
12. Vladimir A. Kazakov, Matthias Staudacher, and Thomas Wynter. Almost flat planar diagrams. Comm. Math. Phys., 179 (1) : 235-256, 1996. MR1395223 (98e:82032) (Pubitemid 126086217)
13. Vladimir A. Kazakov, Matthias Staudacher, and Thomas Wynter. Character expansion methods for matrix models of dually weighted graphs. Comm. Math. Phys., 177 (2) : 451-468, 1996. MR1384144 (97b:81083) (Pubitemid 126321938)
14. Greg Kuperberg. Random words, quantum statistics, central limits, random matrices. Methods Appl. Anal., 9 (1) : 99-118, 2002. MR1948465 (2003k:60020) (Pubitemid 36260355)
15. Greg Kuperberg. A tracial quantum central limit theorem. Trans. Amer. Math. Soc., 357 (2) : 459-471 (electronic), 2005. MR2095618 (2005k:46171) (Pubitemid 40251538)
16. Peter Littelmann. Paths and root operators in representation theory. Ann. of Math. (2), 142 (3) : 499-525, 1995. MR1356780 (96m:17011) (Pubitemid 126006792)
17. Madan Lal Mehta. Random matrices. Academic Press Inc., Boston, MA, second edition, 1991. MR1083764 (92f:82002)
18. Paul-André Meyer. Quantum probability for probabilists, volume 1538 of Lecture Notes in Mathematics. Springer-Verlag, Berlin, 1993. MR1222649 (94k:81152)
19. Marc A. Rieffel. Gromov-Hausdorff distance for quantum metric spaces. Matrix algebras converge to the sphere for quantum Gromov-Hausdorff distance. American Mathematical Society, Providence, RI, 2004. Mem. Amer. Math. Soc. 168 (2004), no. 796. MR2055927
20. Piotr Śniady. Gaussian fluctuations of characters of symmetric groups and of Young diagrams. Probab. Theory Related Fields, 136 (2) : 263-297, 2006. MR2240789 (2007d:20020) (Pubitemid 44121034)
21. Piotr Śniady and Roland Speicher. Permutationally invariant random matrices. In preparation, 2008.
22. D. V. Voiculescu, K. J. Dykema, and A. Nica. Free random variables. American Mathematical Society, Providence, RI, 1992. MR1217253 (94c:46133)
23. S. L. Woronowicz. Compact matrix pseudogroups. Comm. Math. Phys., 111 (4) : 613-665, 1987. MR901157 (88m:46079)