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Volumn 55, Issue 1, 2005, Pages 127-133

Free probability and the von Neumann algebras of free groups

Author keywords

Free entropy dimension; Free group factors; Free independence; Noncommutative probability; von Neumann factors

Indexed keywords


EID: 18144375565     PISSN: 00344877     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0034-4877(05)80008-4     Document Type: Article
Times cited : (27)

References (27)
  • 1
    • 0038129894 scopus 로고    scopus 로고
    • Large deviation bounds for matrix Brownian motion
    • P. Biane M. Capitaine A. Guionnet Large deviation bounds for matrix Brownian motion Invent. Math. 152 2003 433-459
    • (2003) Invent. Math. , vol.152 , pp. 433-459
    • Biane, P.1    Capitaine, M.2    Guionnet, A.3
  • 2
    • 0001757439 scopus 로고
    • 2-chommology and group chomology
    • 2-chommology and group chomology Topology 25 1986 189-215
    • (1986) Topology , vol.25 , pp. 189-215
    • Cheeger, J.1    Gromov, M.2
  • 3
    • 0002179940 scopus 로고
    • Classification of injective factors
    • A. Connes Classification of injective factors Ann. of Math. 104 1976 73-115
    • (1976) Ann. of Math. , vol.104 , pp. 73-115
    • Connes, A.1
  • 4
    • 23744514496 scopus 로고    scopus 로고
    • 2-homology for von Neumann algebras
    • preprint, math.OA/0309343
    • 2-homology for von Neumann algebras, preprint, math.OA/0309343.
    • Connes, A.1    Shlyakhtenko, D.2
  • 5
    • 84973997755 scopus 로고
    • Free products of hyperfinite von Neumann algebras and free dimension
    • K.J. Dykema Free products of hyperfinite von Neumann algebras and free dimension Duke Math. J. 69 1993 97-119
    • (1993) Duke Math. J. , vol.69 , pp. 97-119
    • Dykema, K.J.1
  • 6
    • 84972580950 scopus 로고
    • Interpolated free group factors
    • K.J. Dykema Interpolated free group factors Pacific J. Math. 163 1994 123-135
    • (1994) Pacific J. Math. , vol.163 , pp. 123-135
    • Dykema, K.J.1
  • 7
    • 0032386640 scopus 로고    scopus 로고
    • Applications of free entropy to finite von Neumann algebras, II
    • L. Ge Applications of free entropy to finite von Neumann algebras, II Ann. of Math. 147 1998 143-157
    • (1998) Ann. of Math. , vol.147 , pp. 143-157
    • Ge, L.1
  • 8
    • 0242710877 scopus 로고    scopus 로고
    • A free entropy dimension lemma
    • K. Jung A free entropy dimension lemma Pacific J. Math. 177 2003 265-271
    • (2003) Pacific J. Math. , vol.177 , pp. 265-271
    • Jung, K.1
  • 9
    • 18144394436 scopus 로고    scopus 로고
    • Baton Rouge problem list on operator algebras
    • R. V Kadison: Baton Rouge problem list on operator algebras.
    • Kadison, R.V.1
  • 10
    • 18144431835 scopus 로고    scopus 로고
    • Non-microstates free entropy dimension for groups
    • preprint
    • I. Mineyev and D. Shlyakhtenko: Non-microstates free entropy dimension for groups, preprint.
    • Mineyev, I.1    Shlyakhtenko, D.2
  • 12
    • 14944349453 scopus 로고    scopus 로고
    • Solid von Neumann algebras
    • N. Ozawa Solid von Neumann algebras Acta Math. 192 2004 111-117
    • (2004) Acta Math. , vol.192 , pp. 111-117
    • Ozawa, N.1
  • 13
    • 0000694316 scopus 로고
    • ∞) ⊗ B(H) scaling the trace
    • Serie I t
    • ∞) ⊗ B(H) scaling the trace C.R. Acad. Sci. Paris Serie I t. 314 1992 1027-1032
    • (1992) C.R. Acad. Sci. Paris , vol.314 , pp. 1027-1032
    • Rǎdulescu, F.1
  • 14
    • 0001018420 scopus 로고
    • Random matrices, amalgamated free products and subfactors of the von Neumann algebra of a free group
    • F. Rǎdulescu Random matrices, amalgamated free products and subfactors of the von Neumann algebra of a free group Invent. Math. 115 1994 347-389
    • (1994) Invent. Math. , vol.115 , pp. 347-389
    • Rǎdulescu, F.1
  • 15
    • 0001217416 scopus 로고    scopus 로고
    • Free quasi-free states
    • D. Shlyakhtenko Free quasi-free states Pacific J. Math. 177 1997 329-368
    • (1997) Pacific J. Math. , vol.177 , pp. 329-368
    • Shlyakhtenko, D.1
  • 16
    • 0001146474 scopus 로고
    • Symmetries of some reduced free product C*-algebras
    • Operator algebras and their connections with topology and ergodic theory Springer
    • D. Voiculescu Symmetries of some reduced free product C*-algebras Operator algebras and their connections with topology and ergodic theory Lecture Notes in Math. 1132 1985 Springer 556-588
    • (1985) Lecture Notes in Math. , vol.1132 , pp. 556-588
    • Voiculescu, D.1
  • 17
    • 0003375423 scopus 로고
    • Circular and semicircular systems and free product factors
    • Operator algebras, unitary representations, enveloping algebras and invariant theory (Birkhäuser,MA 1990)
    • D. Voiculescu Circular and semicircular systems and free product factors Operator algebras, unitary representations, enveloping algebras and invariant theory Progr. Math. 92 1990 (Birkhäuser, MA 1990) 45-60
    • (1990) Progr. Math. , vol.92 , pp. 45-60
    • Voiculescu, D.1
  • 18
    • 0000215544 scopus 로고
    • Limit laws for random matrices and free products
    • D. Voiculescu Limit laws for random matrices and free products Invent. Math. 104 1991 201-220
    • (1991) Invent. Math. , vol.104 , pp. 201-220
    • Voiculescu, D.1
  • 19
    • 0000523766 scopus 로고
    • The analogues of entropy and of Fisher's information measure in free probability theory, II
    • D. Voiculescu The analogues of entropy and of Fisher's information measure in free probability theory, II Invent. Math. 118 1994 411-440
    • (1994) Invent. Math. , vol.118 , pp. 411-440
    • Voiculescu, D.1
  • 20
    • 0030544382 scopus 로고    scopus 로고
    • The analogues of entropy and of Fisher's information measure in free probability theory, III: The absence of Cartan subalgebras
    • D. Voiculescu 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
    • (1996) Geom. Funct. Anal. , vol.6 , pp. 172-199
    • Voiculescu, D.1
  • 21
    • 0032380955 scopus 로고    scopus 로고
    • The analogues of entropy and of Fisher's information measure in free probability theory
    • V: Noncommutative Hilbert transforms
    • D. Voiculescu The analogues of entropy and of Fisher's information measure in free probability theory, V: Noncommutative Hilbert transforms Invent. Math. 132 1998 182-227
    • (1998) Invent. Math. , vol.132 , pp. 182-227
    • Voiculescu, D.1
  • 22
    • 1842679304 scopus 로고    scopus 로고
    • A strengthened asymptotic freeness result for random matrices with applications to free entropy
    • D. Voiculescu A strengthened asymptotic freeness result for random matrices with applications to free entropy Internat. Math. Res. Notices 1 1998 43-64
    • (1998) Internat. Math. Res. Notices , vol.1 , pp. 43-64
    • Voiculescu, D.1
  • 26
    • 0003385937 scopus 로고
    • Free probability theory: Random matrices and von Neumann algebras
    • Zürich 1994 1995 Birkhäuser Providence, RI
    • D. Voiculescu Free probability theory: Random matrices and von Neumann algebras Proceedings Internat. Congr of Mathematicians Zürich 1994 1995 Birkhäuser Providence, RI 227-241
    • (1995) Proceedings Internat. Congr. of Mathematicians , pp. 227-241
    • Voiculescu, D.1
  • 27
    • 0003251321 scopus 로고    scopus 로고
    • Lectures on free probability theory
    • École d'Été de Probabilités de Saint-Flour XXVII Lecture Notes in Math. 1738 (Springer)
    • D. Voiculescu Lectures on free probability theory,in Lectures on Probability Theory and Statistics,École d'Été de Probabilités de Saint-Flour XXVII Lecture Notes in Math. 1738 1998 Springer 280-349
    • (1998) Lectures on Probability Theory and Statistics , pp. 280-349
    • Voiculescu, D.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.