@article{AIHPB_2000__36_1_71_0, author = {Hiai, Fumio and Petz, D\'enes}, title = {A large deviation theorem for the empirical eigenvalue distribution of random unitary matrices}, journal = {Annales de l'I.H.P. Probabilit\'es et statistiques}, volume = {36}, year = {2000}, pages = {71-85}, mrnumber = {1743092}, zbl = {0954.60030}, language = {en}, url = {http://dml.mathdoc.fr/item/AIHPB_2000__36_1_71_0} }
Hiai, Fumio; Petz, Dénes. A large deviation theorem for the empirical eigenvalue distribution of random unitary matrices. Annales de l'I.H.P. Probabilités et statistiques, Tome 36 (2000) pp. 71-85. http://gdmltest.u-ga.fr/item/AIHPB_2000__36_1_71_0/
[1] Large deviation for Wigner's law and Voiculescu's non commutative entropy, Probab. Theory Related Fields 108 (1997) 517-542. | MR 1465640 | Zbl 0954.60029
and ,[2] Harmonic Analysis on Semigroups. Theory of Positive Definite and Related Functions, Springer, New York, 1984. | MR 747302 | Zbl 0619.43001
, and ,[3] Large Deviations Techniques and Applications, Jones and Bartlett, Boston, 1993. | MR 1202429 | Zbl 0793.60030
and ,[4] Possible third-order phase transition in the large-N lattice gauge theory, Phys. Rev. D21 (1980) 446-453.
and ,[5] Maximizing free entropy, Acta Math. Hungar. 80 (1998) 325-346. | MR 1645292 | Zbl 0913.94003
and ,[6] The Semicircle Law, Free Random Variables and Entropy, to be published.
and ,[7] Properties of free entropy related to polar decomposition, Comm. Math. Phys. 202 (1999) 421-444. | MR 1690034 | Zbl 0934.46063
and ,[8] Introduction to Hp Spaces, Cambridge Univ. Press, Cambridge, 1980. | MR 565451 | Zbl 0435.30001
,[9] Foundations of Modern Potential Theory, Springer, Berlin, 1972. (Translated from the Russian). | MR 350027 | Zbl 0253.31001
,[10] Random Matrices, Academic Press, Boston, 1991. | MR 1083764 | Zbl 0780.60014
,[11] The analogues of entropy and of Fisher's information measure in free probability theory, I, Comm. Math. Phys. 155 (1993) 71-92. | MR 1228526 | Zbl 0781.60006
,[12] The analogues of entropy and of Fisher's information measure in free probability theory, II, Invent. Math. 118 (1994) 411-440. | MR 1296352 | Zbl 0820.60001
,[13] The analogues of entropy and of Fisher's information measure in free probability theory III: The absence of Cartan subalgebras, Geom. Funct. Anal. 6 ( 1996) 172-199. | MR 1371236 | Zbl 0856.60012
,[14] Free Random Variables, CRM Monograph Ser., Vol. 1, Amer. Math. Soc., 1992. | MR 1217253 | Zbl 0795.46049
, and ,