Gaussian random band matrices and operator-valued free probability theory

Dimitri Shlyakhtenko

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Gaussian random band matrices and operator-valued free probability theory

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Department of Mathematics, University of California, Berkeley, California 94720, U.S.A.

S. R. Bahcall, Random matrix model for superconductors in a magnetic field, to appear in Phys. Rev. Letters.
B. Blackadar, K-theory for operator algebras, Springer-Verlag, 1986.
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.
G. Casati and V. Girko, Generalized Wigner law for band random matrices, Random Oper. and Stoch. Equ. 1 (1993), 279-286.
G. Casati, V. Girko and L. Molinari, Equations for limit functions of band random matrices, Random Oper. and Stoch. Equ. 1 (1993), 91-94.
K. Dykema, On certain free product factors via an extended matrix model, J. Funct. Anal. 112 (1993), 31-60.
F. M. Goodman, R. de la Harpe and V. F. R. Jones, Coxeter graphs and towers of algebras, Springer-Verlag, 1989.
V. F. R. Jones, Index for subfactors, Invent. math. 72 (1983), 1-25.
M. L. Mehta, Random matrices, Academic Press, 1991.
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.
M. Pimsner, A class of C*-algebras generalizing both Cuntz-Krieger algebras and crossed products by , in: D.-V. Voiculescu (ed.), Free Probability, Fields Institute Communications, vol. 12, American Mathematical Society, 1997, pp. 189-212.
S. Popa, Markov traces on universal Jones algebras and subfactors of finite index, Invent. math. 111 (1993), 375-405.
F. Rădulescu, A one parameter group of automorphisms of $L (F_{\infty}) \otimes B (ℋ)$ scaling the trace, C. R. Acad. Sci. Paris 314 (1992), 1027-1032.
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.
F. Rădulescu, A type $I I I_{λ}$ 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.
D. Shlyakhtenko, Random Gaussian band matrices and freeness with amalgamation, Internat. Math. Res. Notices 20 (1996), 1013-1026.
D. Shlyakhtenko, Some applications of freeness with amalgamation, J. Reine Angew. Math. 500 (1998), 191-212.
D. Shlyakhtenko, A-valued semicircular systems, preprint, 1997.
D. Shlyakhtenko, Free quasi-free states, Pacific J. Math. 177 (1997), 329-368.
R. Speicher, Combinatorial theory of the free product with amalgamation and operator-valued free probability theory, Mem. Amer. Math. Soc. 132 (1998).
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.
D.-V. Voiculescu, Addition of certain non-commuting random variables, J. Funct. Anal. 17 (1986), 323-345.
D.-V. Voiculescu, Free noncommutative random variables, random matrices and the $I I_{1}$ factors of free groups, in: Quantum probability and related topics, QP-PQ, VI, World Sci. Publishing, River Edge, NJ, 1991, pp. 473-487.
D.-V. Voiculescu, Limit laws for random matrices and free products, Invent. math. 104 (1991), 201-220.
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.
D.-V. Voiculescu, K. Dykema and A. Nica, Free random variables, CRM monograph series, vol. 1, American Mathematical Society, 1992.

Title

Gaussian random band matrices and operator-valued free probability theory

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