Gaussian random band matrices and operator-valued free probability theory
Shlyakhtenko, Dimitri
Banach Center Publications, Tome 43 (1998), p. 359-368 / Harvested from The Polish Digital Mathematics Library
Publié le : 1998-01-01
EUDML-ID : urn:eudml:doc:208857
@article{bwmeta1.element.bwnjournal-article-bcpv43i1p359bwm,
     author = {Shlyakhtenko, Dimitri},
     title = {Gaussian random band matrices and operator-valued free probability theory},
     journal = {Banach Center Publications},
     volume = {43},
     year = {1998},
     pages = {359-368},
     zbl = {0937.46058},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv43i1p359bwm}
}
Shlyakhtenko, Dimitri. Gaussian random band matrices and operator-valued free probability theory. Banach Center Publications, Tome 43 (1998) pp. 359-368. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv43i1p359bwm/

[000] [1] S. R. Bahcall, Random matrix model for superconductors in a magnetic field, to appear in Phys. Rev. Letters.

[001] [2] B. Blackadar, K-theory for operator algebras, Springer-Verlag, 1986. | Zbl 0597.46072

[002] [3] L. V. Bogachev, S. A. Molchanov and L. A. Pastur, On the density of states of random band matrices, Math. Notes 50 (1991), 1232-1242. | Zbl 0778.60008

[003] [4] G. Casati and V. Girko, Generalized Wigner law for band random matrices, Random Oper. and Stoch. Equ. 1 (1993), 279-286. | Zbl 0839.60035

[004] [5] G. Casati, V. Girko and L. Molinari, Equations for limit functions of band random matrices, Random Oper. and Stoch. Equ. 1 (1993), 91-94. | Zbl 0842.60032

[005] [6] K. Dykema, On certain free product factors via an extended matrix model, J. Funct. Anal. 112 (1993), 31-60. | Zbl 0768.46039

[006] [7] F. M. Goodman, R. de la Harpe and V. F. R. Jones, Coxeter graphs and towers of algebras, Springer-Verlag, 1989. | Zbl 0698.46050

[007] [8] V. F. R. Jones, Index for subfactors, Invent. math. 72 (1983), 1-25. | Zbl 0508.46040

[008] [9] M. L. Mehta, Random matrices, Academic Press, 1991.

[009] [10] L. Pastur, Eigenvalue distribution of random operators and matrices, Séminaire Bourbaki, vol. 1991/92, No. 206, Exp. No. 758, 5, Astérisque, 1993, pp. 445-461. | Zbl 0790.35081

[010] [11] M. Pimsner, A class of C*-algebras generalizing both Cuntz-Krieger algebras and crossed products by 𝒁, in: D.-V. Voiculescu (ed.), Free Probability, Fields Institute Communications, vol. 12, American Mathematical Society, 1997, pp. 189-212. | Zbl 0871.46028

[011] [12] S. Popa, Markov traces on universal Jones algebras and subfactors of finite index, Invent. math. 111 (1993), 375-405. | Zbl 0787.46047

[012] [13] F. Rădulescu, A one parameter group of automorphisms of L(F)B() scaling the trace, C. R. Acad. Sci. Paris 314 (1992), 1027-1032. | Zbl 0810.46073

[013] [14] F. Rădulescu, Random matrices, amalgamated free products and subfactors of the von Neumann algebra of a free group, of noninteger index, Invent. math. 115 (1994), 347-389. | Zbl 0861.46038

[014] [15] F. Rădulescu, A type IIIλ factor with core isomorphic to the von Neumann algebra of a free group, tensor B(H), in: Recent advances in operator algebras (Orléans, 1992), no. 232, Astérisque, 1995, pp. 203-209.

[015] [16] D. Shlyakhtenko, Random Gaussian band matrices and freeness with amalgamation, Internat. Math. Res. Notices 20 (1996), 1013-1026. | Zbl 0872.15018

[016] [17] D. Shlyakhtenko, Some applications of freeness with amalgamation, J. Reine Angew. Math. 500 (1998), 191-212. | Zbl 0926.46046

[017] [18] D. Shlyakhtenko, A-valued semicircular systems, preprint, 1997. | Zbl 0951.46035

[018] [19] D. Shlyakhtenko, Free quasi-free states, Pacific J. Math. 177 (1997), 329-368. | Zbl 0882.46026

[019] [20] R. Speicher, Combinatorial theory of the free product with amalgamation and operator-valued free probability theory, Mem. Amer. Math. Soc. 132 (1998). | Zbl 0935.46056

[020] [21] D.-V. Voiculescu, Symmetries of some reduced free product C*-algebras, in: Operator Algebras and Their Connections with Topology and Ergodic Theory, Lecture Notes in Mathematics, vol. 1132, Springer Verlag, 1985, pp. 556-588.

[021] [22] D.-V. Voiculescu, Addition of certain non-commuting random variables, J. Funct. Anal. 17 (1986), 323-345. | Zbl 0651.46063

[022] [23] D.-V. Voiculescu, Free noncommutative random variables, random matrices and the II1 factors of free groups, in: Quantum probability and related topics, QP-PQ, VI, World Sci. Publishing, River Edge, NJ, 1991, pp. 473-487. | Zbl 0928.46045

[023] [24] D.-V. Voiculescu, Limit laws for random matrices and free products, Invent. math. 104 (1991), 201-220. | Zbl 0736.60007

[024] [25] D.-V. Voiculescu, Operations on certain non-commutative operator-valued random variables, in: Recent advances in operator algebras (Orléans, 1992), no. 232, Astérisque, 1995, pp. 243-275.

[025] [26] D.-V. Voiculescu, K. Dykema and A. Nica, Free random variables, CRM monograph series, vol. 1, American Mathematical Society, 1992. | Zbl 0795.46049