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Volumn 55, Issue 5, 2000, Pages 923-975

Determinantal random point fields

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EID: 0034556390     PISSN: 00360279     EISSN: 14684829     Source Type: Journal    
DOI: 10.1070/RM2000v055n05ABEH000321     Document Type: Article
Times cited : (439)

References (96)
  • 1
    • 0002516103 scopus 로고
    • Correlation functions and the uniqueness of the state in classical statistical mechanics
    • A. Lenard, "Correlation functions and the uniqueness of the state in classical statistical mechanics", Comm. Math. Phys. 30 (1973), 35-44.
    • (1973) Comm. Math. Phys. , vol.30 , pp. 35-44
    • Lenard, A.1
  • 2
    • 0016621185 scopus 로고
    • States of classical statistical mechanical systems of infinitely many particles. I
    • A. Lenard, "States of classical statistical mechanical systems of infinitely many particles. I", Arch. Rational Mech. Anal. 59 (1975), 219-239.
    • (1975) Arch. Rational Mech. Anal. , vol.59 , pp. 219-239
    • Lenard, A.1
  • 3
    • 0016623758 scopus 로고
    • States of classical statistical mechanical systems of infinitely many particles. II
    • A. Lenard, "States of classical statistical mechanical systems of infinitely many particles. II", Arch. Rational Mech. Anal. 59 (1975), 240-256.
    • (1975) Arch. Rational Mech. Anal. , vol.59 , pp. 240-256
    • Lenard, A.1
  • 4
    • 85163698931 scopus 로고
    • Russian transl. from the German, Nauka, Moscow 2nd ed. English transl. from the German, Chelsea, New York 1956
    • A. N. Kolmogorov, The foundations of the theory of probability, 2nd ed., Russian transl. from the German, Nauka, Moscow 1974; 2nd ed. English transl. from the German, Chelsea, New York 1956.
    • (1974) The Foundations of the Theory of Probability, 2nd Ed.
    • Kolmogorov, A.N.1
  • 6
    • 85164654876 scopus 로고
    • English transl., Edinburgh-London
    • N. I. Akhiezer, The classical moment problem and some related questions in analysis, Fizmatlit, Moscow 1961; English transl., Oliver & Boyd, Edinburgh-London 1965.
    • (1965) Oliver & Boyd
  • 7
    • 0002672593 scopus 로고    scopus 로고
    • The classical moment problem as a self-adjoint finite difference operator
    • B. Simon, "The classical moment problem as a self-adjoint finite difference operator", Adv. in Math. 137 (1998), 82-203.
    • (1998) Adv. in Math. , vol.137 , pp. 82-203
    • Simon, B.1
  • 8
    • 0016486888 scopus 로고
    • The coincidence approach to stochastic point processes
    • O. Macchi, "The coincidence approach to stochastic point processes", Adv. Appl. Probab. 7 (1975), 83-122.
    • (1975) Adv. Appl. Probab. , vol.7 , pp. 83-122
    • Macchi, O.1
  • 10
    • 85164641549 scopus 로고    scopus 로고
    • personal communications
    • B. Simon, personal communications.
    • Simon, B.1
  • 11
    • 21344496244 scopus 로고
    • Charge deficiency, charge transport and comparison of dimensions
    • J. E. Avron, R. Seiler, and B. Simon, "Charge deficiency, charge transport and comparison of dimensions", Comm. Math. Phys. 159 (1994), 399-422.
    • (1994) Comm. Math. Phys. , vol.159 , pp. 399-422
    • Avron, J.E.1    Seiler, R.2    Simon, B.3
  • 13
    • 0003744099 scopus 로고
    • English transl., Providence, RI
    • I. Ts. Gokhberg and M. G. Krein, Introduction to the theory of linear non-self-adjoint operators, Nauka, Moscow 1965; English transl., Amer. Math. Soc., Providence, RI 1969.
    • (1969) Amer. Math. Soc.
  • 14
    • 0003687441 scopus 로고
    • Vols. I-IV, Academic Press, New York Russian transl., Mir, Moscow 1977, 1978, 1982, 1982
    • M. Reed and B. Simon, Methods of modern mathematical physics, Vols. I-IV, Academic Press, New York 1975-1980; Russian transl., Mir, Moscow 1977, 1978, 1982, 1982.
    • (1975) Methods of Modern Mathematical Physics
    • Reed, M.1    Simon, B.2
  • 16
    • 0032163852 scopus 로고    scopus 로고
    • Correlation functions, cluster functions and spacing distribution for random matrices
    • C. A. Tracy and H. Widom, "Correlation functions, cluster functions and spacing distribution for random matrices", J. Statist. Phys. 92 (1998), 809-835.
    • (1998) J. Statist. Phys. , vol.92 , pp. 809-835
    • Tracy, C.A.1    Widom, H.2
  • 19
    • 35549006412 scopus 로고
    • Statistical theory of the energy levels of complex systems. I
    • F. J. Dyson, "Statistical theory of the energy levels of complex systems. I", J. Math. Phys. 3 (1962), 140-156.
    • (1962) J. Math. Phys. , vol.3 , pp. 140-156
    • Dyson, F.J.1
  • 20
    • 0141913605 scopus 로고
    • Statistical theory of the energy levels of complex systems. II
    • F. J. Dyson, "Statistical theory of the energy levels of complex systems. II", J. Math. Phys. 3 (1962), 157-165.
    • (1962) J. Math. Phys. , vol.3 , pp. 157-165
    • Dyson, F.J.1
  • 21
    • 0242436583 scopus 로고
    • Statistical theory of the energy levels of complex systems. III
    • F. J. Dyson, "Statistical theory of the energy levels of complex systems. III", J. Math. Phys. 3 (1962), 166-175.
    • (1962) J. Math. Phys. , vol.3 , pp. 166-175
    • Dyson, F.J.1
  • 22
    • 0142053350 scopus 로고
    • Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons
    • A. Lenard, "Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons", J. Math. Phys. 5 (1964), 930-943.
    • (1964) J. Math. Phys. , vol.5 , pp. 930-943
    • Lenard, A.1
  • 23
    • 0000799156 scopus 로고
    • One-dimensional impenetrable bosons in thermal equilibrium
    • A. Lenard, "One-dimensional impenetrable bosons in thermal equilibrium", J. Math. Phys. 7 (1966), 1268-1272.
    • (1966) J. Math. Phys. , vol.7 , pp. 1268-1272
    • Lenard, A.1
  • 24
    • 0001362231 scopus 로고
    • Interacting Brownian particles: A study of Dyson's model
    • Minneapolis/Minn, G. Papanicolau, ed., Springer-Verlag, New York
    • H. Spohn, "Interacting Brownian particles: A study of Dyson's model", Hydrodynamic Behavior and Interacting Particle Systems, Proc. Workshop, Minneapolis/Minn, 1986 (G. Papanicolau, ed.), Springer-Verlag, New York 1987, pp. 151-179.
    • (1986) Hydrodynamic Behavior and Interacting Particle Systems, Proc. Workshop , pp. 151-179
    • Spohn, H.1
  • 25
    • 0001703129 scopus 로고
    • Statistical ensembles of complex, quaternion and real matrices
    • J. Ginibre, "Statistical ensembles of complex, quaternion and real matrices", J. Math. Phys. 6 (1965), 440-449.
    • (1965) J. Math. Phys. , vol.6 , pp. 440-449
    • Ginibre, J.1
  • 26
    • 0000055699 scopus 로고
    • Exact results for the two-dimensional one-component plasma
    • B. Jancovici, "Exact results for the two-dimensional one-component plasma", Phys. Rev. Lett. 46 (1981), 386-388.
    • (1981) Phys. Rev. Lett. , vol.46 , pp. 386-388
    • Jancovici, B.1
  • 27
    • 0001397067 scopus 로고
    • Classical coulomb systems near a plane wall. I
    • B. Jancovici, "Classical Coulomb systems near a plane wall. I", J. Statist. Phys. 28 (1982), 43-65.
    • (1982) J. Statist. Phys. , vol.28 , pp. 43-65
    • Jancovici, B.1
  • 28
    • 0021575454 scopus 로고
    • The two-dimensional one-component plasma in an inhomogeneous background - Exact results
    • A. Alastuey and J. L. Lebowitz, "The two-dimensional one-component plasma in an inhomogeneous background - exact results", J. Physique 45 (1984), 1859-1874.
    • (1984) J. Physique , vol.45 , pp. 1859-1874
    • Alastuey, A.1    Lebowitz, J.L.2
  • 29
    • 0000917560 scopus 로고
    • Laughlin wave-functions, coulomb gases and expansions of the discriminant
    • F. Di Francesco, M. Gaudin, C. Itzykson, and F. Lesage, "Laughlin wave-functions, Coulomb gases and expansions of the discriminant", Internat. J. Modern Phys. A 9 (1994), 4257-4351.
    • (1994) Internat. J. Modern Phys. A , vol.9 , pp. 4257-4351
    • Francesco, F.D.1    Gaudin, M.2    Itzykson, C.3    Lesage, F.4
  • 30
    • 0001616571 scopus 로고    scopus 로고
    • Two-dimensional one-component plasma in quadrupolar field
    • P. J. Forrester and B. Jancovici, "Two-dimensional one-component plasma in quadrupolar field", Internat. J. Modern Phys. A 11 (1996), 941-949.
    • (1996) Internat. J. Modern Phys. A , vol.11 , pp. 941-949
    • Forrester, P.J.1    Jancovici, B.2
  • 31
    • 0022101562 scopus 로고
    • Critical isotherm of a lattice plasma
    • M. Gaudin, "Critical isotherm of a lattice plasma", J. Physique 46 (1985), 1027-1042.
    • (1985) J. Physique , vol.46 , pp. 1027-1042
    • Gaudin, M.1
  • 32
    • 0002720913 scopus 로고
    • On the two-dimensional coulomb gas
    • F. Cornu and B. Jancovici, "On the two-dimensional Coulomb gas", J. Statist. Phys. 49 (1987), 33-56.
    • (1987) J. Statist. Phys. , vol.49 , pp. 33-56
    • Cornu, F.1    Jancovici, B.2
  • 33
    • 84956132227 scopus 로고
    • Two-dimensional coulomb systems - A larger class of solvable models
    • F. Cornu and B. Jancovici, "Two-dimensional Coulomb systems - A larger class of solvable models", Europhys. Lett. 5 (1988), 125-128.
    • (1988) Europhys. Lett. , vol.5 , pp. 125-128
    • Cornu, F.1    Jancovici, B.2
  • 34
    • 0001305432 scopus 로고
    • Electrical double layer: A solvable model
    • F. Cornu and B. Jancovici, "Electrical double layer: A solvable model", J. Chem. Phys. 90 (1989), 2444-2452.
    • (1989) J. Chem. Phys. , vol.90 , pp. 2444-2452
    • Cornu, F.1    Jancovici, B.2
  • 35
    • 21844516576 scopus 로고
    • Correlations in two-component log-gas systems
    • A. Alastuey and P. J. Forrester, "Correlations in two-component log-gas systems", J. Statist. Phys. 81 (1995), 579-627.
    • (1995) J. Statist. Phys. , vol.81 , pp. 579-627
    • Alastuey, A.1    Forrester, P.J.2
  • 36
    • 21144471795 scopus 로고
    • On the average distance between particles in the 2-dimensional 2-component plasma
    • P. J. Forrester and B. Jancovici, "On the average distance between particles in the 2-dimensional 2-component plasma", J. Statist. Phys. 69 (1992), 163-178.
    • (1992) J. Statist. Phys. , vol.69 , pp. 163-178
    • Forrester, P.J.1    Jancovici, B.2
  • 39
    • 0031525857 scopus 로고    scopus 로고
    • On random matrices from the compact classical groups
    • K. Johansson, "On random matrices from the compact classical groups", Ann. of Math. (2) 145 (1997), 519-545.
    • (1997) Ann. of Math. , vol.145 , Issue.2 , pp. 519-545
    • Johansson, K.1
  • 40
    • 0001891773 scopus 로고
    • On the eigenvalues of random matrices
    • Studies in Appl. Probab., Essays in honour of Lajos Takacs Special Volume
    • P. Diaconis and M. Shahshahani, "On the eigenvalues of random matrices", (Studies in Appl. Probab., Essays in honour of Lajos Takacs) J. Appl. Probab., (Special Volume) 31A (1994), 49-62.
    • (1994) J. Appl. Probab. , vol.31 A , pp. 49-62
    • Diaconis, P.1    Shahshahani, M.2
  • 42
    • 0032285810 scopus 로고    scopus 로고
    • Level spacings distribution for large random matrices: Gaussian fluctuations
    • A. Soshnikov, "Level spacings distribution for large random matrices: Gaussian fluctuations", Ann. of Math. (2) 148 (1998), 573-617.
    • (1998) Ann. of Math. , vol.148 , Issue.2 , pp. 573-617
    • Soshnikov, A.1
  • 43
    • 85164647857 scopus 로고    scopus 로고
    • Gaussian fluctuations for the number of particles in airy, bessel, sine and other determinantal random point fields
    • to appear
    • A. Soshnikov, "Gaussian fluctuations for the number of particles in Airy, Bessel, sine and other determinantal random point fields", http://xxx.lanl.gov/abs/math-ph/9907012 (to appear in J. Statist. Phys. 100).
    • J. Statist. Phys. , pp. 100
    • Soshnikov, A.1
  • 44
    • 85164643432 scopus 로고    scopus 로고
    • Central limit theorem for local linear statistics in classical compact groups and related combinatorial identities
    • to appear
    • A. Soshnikov, "Central limit theorem for local linear statistics in classical compact groups and related combinatorial identities", http://xxx.lanl.gov/math.PR/9908063 (to appear in Ann. Probab.).
    • Ann. Probab.
    • Soshnikov, A.1
  • 45
    • 0039799159 scopus 로고
    • Circle law
    • V. Girko, "Circle law", Teor. Veroyatnost. i Primenen. 29 (1984), 669-679; English transl. in Theory Probab. Appl. 29 (1985), 694-704.
    • (1984) Teor. Veroyatnost. i Primenen. , vol.29 , pp. 669-679
    • Girko, V.1
  • 46
    • 85164640982 scopus 로고
    • English transl.
    • V. Girko, "Circle law", Teor. Veroyatnost. i Primenen. 29 (1984), 669-679; English transl. in Theory Probab. Appl. 29 (1985), 694-704.
    • (1985) Theory Probab. Appl. , vol.29 , pp. 694-704
  • 47
    • 0002111201 scopus 로고
    • Elliptic law
    • V. Girko, "Elliptic law", Teor. Veroyatnost. i Primenen. 30 (1985), 640-651; English transl. in Theory Probab. Appl. 30 (1986), 677-690.
    • (1985) Teor. Veroyatnost. i Primenen. , vol.30 , pp. 640-651
    • Girko, V.1
  • 48
    • 0002111201 scopus 로고
    • English transl.
    • V. Girko, "Elliptic law", Teor. Veroyatnost. i Primenen. 30 (1985), 640-651; English transl. in Theory Probab. Appl. 30 (1986), 677-690.
    • (1986) Theory Probab. Appl. , vol.30 , pp. 677-690
  • 50
    • 4243883592 scopus 로고    scopus 로고
    • Almost Hermitian random matrices: Crossover from Wigner-Dyson to Ginibre eigenvalue statistics
    • Ya. V. Fyodorov, B. A. Khoruzhenko, and H.-J. Sommers, "Almost Hermitian random matrices: Crossover from Wigner-Dyson to Ginibre eigenvalue statistics", Phys. Rev. Lett. 79 (1997), 557-560.
    • (1997) Phys. Rev. Lett. , vol.79 , pp. 557-560
    • Fyodorov, Ya.V.1    Khoruzhenko, B.A.2    Sommers, H.-J.3
  • 52
    • 0000112246 scopus 로고
    • Exponential ensemble for random matrices
    • B. V. Bronk, "Exponential ensemble for random matrices", J. Math. Phys. 6 (1965), 228-237.
    • (1965) J. Math. Phys. , vol.6 , pp. 228-237
    • Bronk, B.V.1
  • 53
    • 0032523672 scopus 로고    scopus 로고
    • Matrices coupled in a chain. I. Eigenvalue correlations
    • B. Eynard and M. L. Mehta, "Matrices coupled in a chain. I. Eigenvalue correlations", J. Phys. A 31 (1998), 4449-4456.
    • (1998) J. Phys. A , vol.31 , pp. 4449-4456
    • Eynard, B.1    Mehta, M.L.2
  • 54
    • 0033439997 scopus 로고    scopus 로고
    • The spectrum of coupled random matrices
    • M. Adler and P. van Moerbeke, "The spectrum of coupled random matrices", Ann. of Math. (2) 149 (1999), 921-976.
    • (1999) Ann. of Math. , vol.149 , Issue.2 , pp. 921-976
    • Adler, M.1    Van Moerbeke, P.2
  • 55
    • 0003025563 scopus 로고
    • Fredholm determinants, differential equations and matrix models
    • C. A. Tracy and H. Widom, "Fredholm determinants, differential equations and matrix models", Comm. Math. Phys. 163 (1994), 33-72.
    • (1994) Comm. Math. Phys. , vol.163 , pp. 33-72
    • Tracy, C.A.1    Widom, H.2
  • 56
    • 27644532196 scopus 로고
    • Level-spacing distributions and the airy kernel
    • C. A. Tracy and H. Widom, "Level-spacing distributions and the Airy kernel", Comm. Math. Phys. 159 (1994), 151-174.
    • (1994) Comm. Math. Phys. , vol.159 , pp. 151-174
    • Tracy, C.A.1    Widom, H.2
  • 57
    • 0342395256 scopus 로고
    • Level-spacing distributions and the Bessel kernel
    • C. A. Tracy and H. Widom, "Level-spacing distributions and the Bessel kernel", Comm. Math. Phys. 161 (1994), 289-309.
    • (1994) Comm. Math. Phys. , vol.161 , pp. 289-309
    • Tracy, C.A.1    Widom, H.2
  • 58
    • 0000609652 scopus 로고
    • The spectrum edge of random matrix ensembles
    • P. J. Forrester, "The spectrum edge of random matrix ensembles", Nucl. Phys. B 402 (1993), 709-728.
    • (1993) Nucl. Phys. B , vol.402 , pp. 709-728
    • Forrester, P.J.1
  • 59
    • 0030684834 scopus 로고    scopus 로고
    • Universality of the local eigenvalue statistics for a class of unitary invariant random matrix ensembles
    • L. Pastur and M. Shcherbina, "Universality of the local eigenvalue statistics for a class of unitary invariant random matrix ensembles", J. Statist. Phys. 86 (1997), 109-147.
    • (1997) J. Statist. Phys. , vol.86 , pp. 109-147
    • Pastur, L.1    Shcherbina, M.2
  • 60
    • 0033244830 scopus 로고    scopus 로고
    • Semiclassical asymptotics of orthogonal polynomials, Riemann-Hilbert problem and universality in the matrix model
    • P. Bleher and A. Its, "Semiclassical asymptotics of orthogonal polynomials, Riemann-Hilbert problem and universality in the matrix model", Ann. of Math. (2) 150 (1999), 185-266.
    • (1999) Ann. of Math. , vol.150 , Issue.2 , pp. 185-266
    • Bleher, P.1    Its, A.2
  • 61
    • 0033440723 scopus 로고    scopus 로고
    • Uniform asymptotics for polynomials orthogonal with respect to varying exponential weights and applications to universality questions in random matrix theory
    • P. Deift, T. Kriecherbauer, K. T.-R. McLaughlin, S. Venakides, and X. Zhou, "Uniform asymptotics for polynomials orthogonal with respect to varying exponential weights and applications to universality questions in random matrix theory", Comm. Pure Appl. Math. 52 (1999), 1335-1425.
    • (1999) Comm. Pure Appl. Math. , vol.52 , pp. 1335-1425
    • Deift, P.1    Kriecherbauer, T.2    McLaughlin, K.T.-R.3    Venakides, S.4    Zhou, X.5
  • 63
    • 0033473406 scopus 로고    scopus 로고
    • Universality at the edge of the spectrum in Wigner random matrices
    • A. Soshnikov, "Universality at the edge of the spectrum in Wigner random matrices", Comm. Math. Phys. 207 (1999), 697-733.
    • (1999) Comm. Math. Phys. , vol.207 , pp. 697-733
    • Soshnikov, A.1
  • 66
    • 0004049898 scopus 로고    scopus 로고
    • Cambridge Univ. Press, Cambridge
    • W. Fulton, Young tableaux, Cambridge Univ. Press, Cambridge 1997.
    • (1997) Young Tableaux
    • Fulton, W.1
  • 72
    • 85037782030 scopus 로고    scopus 로고
    • Distributions on partitions, point processes, and the hypergeometric kernel
    • to appear
    • A. Borodin and G. Olshanski, "Distributions on partitions, point processes, and the hypergeometric kernel", http://xxx.lanl.gov/abs/math/9904010 (to appear in Comm. Math. Phys.).
    • Comm. Math. Phys.
    • Borodin, A.1    Olshanski, G.2
  • 74
    • 0032216968 scopus 로고    scopus 로고
    • Point processes and the infinite symmetric group
    • A. Borodin and G. Olshanski, "Point processes and the infinite symmetric group", Math. Res. Lett. 5 (1998), 799-816.
    • (1998) Math. Res. Lett. , vol.5 , pp. 799-816
    • Borodin, A.1    Olshanski, G.2
  • 75
    • 0001656032 scopus 로고
    • Harmonic analysis on the infinite symmetric group. A deformation of the regular representation
    • S. Kerov, G. Olshanski, and A. Vershik, "Harmonic analysis on the infinite symmetric group. A deformation of the regular representation", C. R. Acad. Sci. Paris Sér. I Math. 316 (1993), 773-778.
    • (1993) C. R. Acad. Sci. Paris Sér. I Math. , vol.316 , pp. 773-778
    • Kerov, S.1    Olshanski, G.2    Vershik, A.3
  • 77
    • 85046526389 scopus 로고    scopus 로고
    • Shape fluctuations and random matrices
    • to appear
    • K. Johansson, "Shape fluctuations and random matrices", http://xxx.lanl.gov/abs/ math/9903134 (to appear in Comm. Math. Phys.).
    • Comm. Math. Phys.
    • Johansson, K.1
  • 79
    • 0033458290 scopus 로고    scopus 로고
    • Longest increasing subsequences: From patience sorting to the Baik-Deift-Johansson theorem
    • N. S.
    • D. Aldous and P. Diaconis, "Longest increasing subsequences: From patience sorting to the Baik-Deift-Johansson theorem", Bull. Amer. Math. Soc. (N. S.) 36 (1999), 413-432.
    • (1999) Bull. Amer. Math. Soc. , vol.36 , pp. 413-432
    • Aldous, D.1    Diaconis, P.2
  • 80
    • 0033443150 scopus 로고    scopus 로고
    • On the distribution of the length of the longest increasing subsequence of random permutations
    • J. Baik, P. A. Deift, and K. Johansson, "On the distribution of the length of the longest increasing subsequence of random permutations", J. Amer. Math. Soc. 12 (1999), 1119-1178.
    • (1999) J. Amer. Math. Soc. , vol.12 , pp. 1119-1178
    • Baik, J.1    Deift, P.A.2    Johansson, K.3
  • 91
    • 0033474974 scopus 로고    scopus 로고
    • Random unitary matrices, permutations and Painlevé
    • C. A. Tracy and H. Widom, "Random unitary matrices, permutations and Painlevé", Comm. Math. Phys. 207 (1999), 665-685.
    • (1999) Comm. Math. Phys. , vol.207 , pp. 665-685
    • Tracy, C.A.1    Widom, H.2
  • 93
    • 0003411523 scopus 로고
    • Nauka, Moscow English transl., Springer-Verlag, New York-Heidelberg-Berlin
    • I. P. Cornfeld, S. V. Fomin, and Ya. G. Sinai, Ergodic theory, Nauka, Moscow 1980; English transl., Springer-Verlag, New York-Heidelberg-Berlin 1982.
    • (1980) Ergodic Theory
    • Cornfeld, I.P.1    Fomin, S.V.2    Sinai, Ya.G.3
  • 95
    • 0002542182 scopus 로고
    • Gaussian fluctuations in random matrices
    • O. Costin and J. Lebowitz, "Gaussian fluctuations in random matrices", Phys. Rev. Lett. 75 (1995), 69-72.
    • (1995) Phys. Rev. Lett. , vol.75 , pp. 69-72
    • Costin, O.1    Lebowitz, J.2


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