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Volumn 118, Issue 3, 2003, Pages 375-425

Microstates free entropy and cost of equivalence relations

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EID: 0038034784     PISSN: 00127094     EISSN: None     Source Type: Journal    
DOI: 10.1215/S0012-7094-03-11831-1     Document Type: Article
Times cited : (5)

References (24)
  • 1
    • 0002003480 scopus 로고
    • Free Brownian motion, free stochastic calculus and random matrices
    • Free Probability Theory (Waterloo, Ontario, 1995), Amer. Math. Soc., Providence. MR 97m:46104
    • P. BIANE, "Free Brownian motion, free stochastic calculus and random matrices" in Free Probability Theory (Waterloo, Ontario, 1995), Fields Inst. Commun. 12, Amer. Math. Soc., Providence, 1997, 1-19. MR 97m:46104
    • (1995) Fields Inst. Commun. , vol.12 , pp. 1-19
    • Biane, P.1
  • 2
    • 84968495052 scopus 로고
    • Ergodic equivalence relations, cohomology, and von Neumann algebras, I
    • MR58:28261a
    • J. FELDMAN and C. C. MOORE, Ergodic equivalence relations, cohomology, and von Neumann algebras, I, Trans. Amer. Math. Soc. 234 (1977), 289-324. MR58:28261a
    • (1977) Trans. Amer. Math. Soc. , vol.234 , pp. 289-324
    • Feldman, J.1    Moore, C.C.2
  • 3
    • 84968503421 scopus 로고
    • Ergodic equivalence relations, cohomology, and von Neumann algebras, II
    • MR58:28261b
    • _, Ergodic equivalence relations, cohomology, and von Neumann algebras, II, Trans. Amer. Math. Soc. 234 (1977), 325-359. MR58:28261b
    • (1977) Trans. Amer. Math. Soc. , vol.234 , pp. 325-359
  • 4
    • 0031627126 scopus 로고    scopus 로고
    • Mercuriale de groupes et de relations
    • MR 99h:28034
    • D. GABORIAU, Mercuriale de groupes et de relations, C. R. Acad. Sci. Paris Sér. I Math. 326 (1998), 219-222. MR 99h:28034
    • (1998) C. R. Acad. Sci. Paris Sér. I Math. , vol.326 , pp. 219-222
    • Gaboriau, D.1
  • 5
    • 0034340697 scopus 로고    scopus 로고
    • Coût des relations d'équivalence et des groupes
    • MR 2001f:28030
    • _, Coût des relations d'équivalence et des groupes, Invent. Math. 139 (2000), 41-98. MR 2001f:28030
    • (2000) Invent. Math. , vol.139 , pp. 41-98
  • 6
    • 0034147221 scopus 로고    scopus 로고
    • 2 des actions préservant une mesure
    • MR 2001d:37004
    • 2 des actions préservant une mesure, C. R. Acad. Sci. Paris. Sér. I Math. 330 (2000), 365-370. MR 2001d:37004
    • (2000) C. R. Acad. Sci. Paris. Sér. I Math. , vol.330 , pp. 365-370
  • 7
    • 0038609785 scopus 로고    scopus 로고
    • 2 de relations d'équivalence et de groupes
    • CMP 1 953 191
    • 2 de relations d'équivalence et de groupes, Inst. Hautes Études Sci. Publ. Math. 95 (2002), 93-150. CMP 1 953 191
    • (2002) Inst. Hautes Études Sci. Publ. Math. , vol.95 , pp. 93-150
  • 8
    • 0032386640 scopus 로고    scopus 로고
    • Applications of free entropy to finite von Neumann algebras. II
    • MR 99c:46068
    • L. GE, Applications of free entropy to finite von Neumann algebras. II, Ann. of Math. (2) 147 (1998), 143-157. MR 99c:46068
    • (1998) Ann. of Math. (2) , vol.147 , pp. 143-157
    • Ge, L.1
  • 9
    • 0034730164 scopus 로고    scopus 로고
    • Free entropy and property T factors
    • MR 2001g:46145
    • L. GE and J. SHEN, Free entropy and property T factors, Proc. Natl. Acad. Sci. USA 97 (2000), 9881-9885. MR 2001g:46145
    • (2000) Proc. Natl. Acad. Sci. USA , vol.97 , pp. 9881-9885
    • Ge, L.1    Shen, J.2
  • 10
    • 0033238571 scopus 로고    scopus 로고
    • Properties of free entropy related to polar decomposition
    • MR 2000h:46080
    • F. HIAI and D. PETZ, Properties of free entropy related to polar decomposition, Comm. Math. Phys. 202 (1999), 421-444. MR 2000h:46080
    • (1999) Comm. Math. Phys. , vol.202 , pp. 421-444
    • Hiai, F.1    Petz, D.2
  • 11
    • 0003348167 scopus 로고
    • Ergodic theory
    • Cambridge Univ. Press, Cambridge, 1983. MR 87i:28002
    • K. PETERSEN, Ergodic Theory, Cambridge Stud. Adv. Math. 2, Cambridge Univ. Press, Cambridge, 1983. MR 87i:28002
    • (1983) Cambridge Stud. Adv. Math. , vol.2
    • Petersen, K.1
  • 12
    • 0032222245 scopus 로고    scopus 로고
    • Some applications of freeness with amalgamation
    • MR 99j:46079
    • D. SHLYAKHTENKO, Some applications of freeness with amalgamation, J. Reine Angew. Math. 500 (1998), 191-212. MR 99j:46079
    • (1998) J. Reine Angew. Math. , vol.500 , pp. 191-212
    • Shlyakhtenko, D.1
  • 13
    • 0035531725 scopus 로고    scopus 로고
    • Free fisher information with respect to a completely positive map and cost of equivalence relations
    • MR 2002e:46077
    • _, Free Fisher information with respect to a completely positive map and cost of equivalence relations, Comm. Math. Phys. 218 (2001), 133-152. MR 2002e:46077
    • (2001) Comm. Math. Phys. , vol.218 , pp. 133-152
  • 15
    • 21144462319 scopus 로고
    • The analogues of entropy and of Fisher's information measure in free probability theory, I
    • MR 94k:46137
    • D. VOICULESCU, The analogues of entropy and of Fisher's information measure in free probability theory, I, Comm. Math. Phys. 155 (1993), 71-92. MR 94k:46137
    • (1993) Comm. Math. Phys. , vol.155 , pp. 71-92
    • Voiculescu, D.1
  • 16
    • 0000523766 scopus 로고
    • The analogues of entropy and of Fisher's information measure in free probability theory, II
    • MR 96a:46117
    • _, The analogues of entropy and of Fisher's information measure in free probability theory, II, Invent. Math. 118 (1994), 411-440. MR 96a:46117
    • (1994) Invent. Math. , vol.118 , pp. 411-440
  • 17
    • 0001089654 scopus 로고
    • Operations on certain non-commutative operator-valued random variables
    • Recent Advances in Operator Algebras (Orléans, France, 1992), Soc. Math. France, Montrouge. MR 97b:46081
    • _, "Operations on certain non-commutative operator-valued random variables" in Recent Advances in Operator Algebras (Orléans, France, 1992), Astérisque 232, Soc. Math. France, Montrouge, 1995, 243-275. MR 97b:46081
    • (1992) Astérisque , vol.232 , pp. 243-275
  • 18
    • 0030544382 scopus 로고    scopus 로고
    • The analogues of entropy and of Fisher's information measure in free probability theory, III: The absence of Cartan subalegras
    • MR 96m:46119
    • _, The analogues of entropy and of Fisher's information measure in free probability theory, III: The absence of Cartan subalegras, Geom. Funct. Anal. 6 (1996), 172-199. MR 96m:46119
    • (1996) Geom. Funct. Anal. , vol.6 , pp. 172-199
  • 19
    • 0000824331 scopus 로고    scopus 로고
    • The analogues of entropy and of Fisher's information measure in free probability theory, IV: Maximum entropy and freeness
    • Free Probability Theory (Waterloo, Ontario, 1995), Amer. Math. Soc., Providence. MR 97j:46071
    • _, "The analogues of entropy and of Fisher's information measure in free probability theory, IV: Maximum entropy and freeness" in Free Probability Theory (Waterloo, Ontario, 1995), Field Inst. Commun. 12, Amer. Math. Soc., Providence, 1997, 293-302. MR 97j:46071
    • (1997) Field Inst. Commun. , vol.12 , pp. 293-302
  • 20
    • 0032380955 scopus 로고    scopus 로고
    • The analogues of entropy and of Fisher's information measure in free probabilility theory, V: Noncommutative Hubert transforms
    • MR 99d:46087
    • _, The analogues of entropy and of Fisher's information measure in free probabilility theory, V: Noncommutative Hubert transforms, Invent. Math. 132 (1998), 189-227. MR 99d:46087
    • (1998) Invent. Math. , vol.132 , pp. 189-227
  • 21
    • 1842679304 scopus 로고    scopus 로고
    • A strengthened asymptotic freeness result for random matrices with applications to free entropy
    • MR 2000d:46080
    • _, A strengthened asymptotic freeness result for random matrices with applications to free entropy. Internat. Math. Res. Notices 1998, no. 1, 41-63. MR 2000d:46080
    • (1998) Internat. Math. Res. Notices , vol.1 , pp. 41-63
  • 22
    • 0033604007 scopus 로고    scopus 로고
    • The analogues of entropy and of Fisher's information measure in free probability, VI: Liberation and mutual free information
    • MR 2001a:46064
    • _, The analogues of entropy and of Fisher's information measure in free probability, VI: Liberation and mutual free information, Adv. Math. 146 (1999), 101-166. MR 2001a:46064
    • (1999) Adv. Math. , vol.146 , pp. 101-166
  • 23
    • 0033419106 scopus 로고    scopus 로고
    • 1
    • MR 2000k:46092
    • 1, J. Reine Angew. Math. 514 (1999), 113-118. MR 2000k:46092
    • (1999) J. Reine Angew. Math. , vol.514 , pp. 113-118
  • 24
    • 0003341428 scopus 로고
    • Free random variables: A noncommutative probability approach to free products with applications to random matrices, operator algebras and harmonic analysis on free groups
    • Amer. Math. Soc., Providence, 1992. MR 94c:46133
    • D. V. VOICULESCU, K. DYKEMA, and A. NICA, Free Random Variables: A Noncommutative Probability Approach to Free Products with Applications to Random Matrices, Operator Algebras and Harmonic Analysis on Free Groups, CRM Monogr. Ser. 1, Amer. Math. Soc., Providence, 1992. MR 94c:46133
    • (1992) CRM Monogr. Ser. , vol.1
    • Voiculescu, D.V.1    Dykema, K.2    Nica, A.3


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