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Volumn 234, Issue 3, 2003, Pages 383-422

Rigorous solution of the Gardner problem

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EID: 0037360747     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00220-002-0783-3     Document Type: Article
Times cited : (73)

References (22)
  • 2
    • 0004340648 scopus 로고    scopus 로고
    • Hopfield models as a generalized random mean field models
    • [B-G]. Mathematical Aspects of Spin Glasses and Neuronal Networks. A. Bovier, P. Picco (eds), Progress in Probability
    • [B-G] Bovier, A., Gayrard, V.: Hopfield models as a generalized random mean field models. Mathematical Aspects of Spin Glasses and Neuronal Networks. A. Bovier, P. Picco (eds), Progress in Probability. Birkhäuser 41, 3-89 (1998)
    • (1998) Birkhäuser , vol.41 , pp. 3-89
    • Bovier, A.1    Gayrard, V.2
  • 3
    • 49549132663 scopus 로고
    • On the extension of the Brunn-Minkowsky and Pekoda-Leindler theorems, includings inequalities for log concave functions, and with an application to the diffusion equation
    • [B-L]
    • [B-L] Brascamp, H.J., Lieb, E.H.: On the extension of the Brunn-Minkowsky and Pekoda-Leindler theorems, includings inequalities for log concave functions, and with an application to the diffusion equation. J. Func. Anall. 22, 366-389 (1976)
    • (1976) J. Func. Anall. , vol.22 , pp. 366-389
    • Brascamp, H.J.1    Lieb, E.H.2
  • 4
    • 4243861085 scopus 로고
    • Random energy model: An exactly solvable model of disordered systems
    • [D]
    • [D] Derrida, B.: Random energy model: An exactly solvable model of disordered systems. Phys. Rev. B24, 2613-2626(1981)
    • (1981) Phys. Rev. , vol.B24 , pp. 2613-2626
    • Derrida, B.1
  • 5
    • 0002631885 scopus 로고
    • Optimal stage properties of neural network models
    • [D-G]
    • [D-G] Derrida, B., Gardner, E.: Optimal stage properties of neural network models. J. Phys. A: Math. Gen. 21, 271-284 (1988)
    • (1988) J. Phys. A: Math. Gen. , vol.21 , pp. 271-284
    • Derrida, B.1    Gardner, E.2
  • 6
    • 36149029786 scopus 로고
    • The space of interactions in neural network models
    • [g]
    • [G] Gardner, E.: The space of interactions in neural network models. J. Phys. A: Math. Gen. 21, 257-270 (1988)
    • (1988) J. Phys. A: Math. Gen. , vol.21 , pp. 257-270
    • Gardner, E.1
  • 9
    • 0003141985 scopus 로고
    • The large-n limit in statistical mechanics and spectral theory of disordered systems
    • [K-K-P-S]. Academic Press
    • [K-K-P-S] Khorunzy, A., Khoruzhenko, B., Pastur, L., Shcherbina, M.: The large-n limit in statistical mechanics and spectral theory of disordered systems. Phase Transition and Critical Phenomena, vol. 15, p. 73, Academic Press, 1992
    • (1992) Phase Transition and Critical Phenomena , vol.15 , pp. 73
    • Khorunzy, A.1    Khoruzhenko, B.2    Pastur, L.3    Shcherbina, M.4
  • 10
    • 0003981320 scopus 로고
    • [Lo]. D. Van Nostrand Comp. Inc.
    • [Lo] Loeve, M.: Probability Theory. D. Van Nostrand Comp. Inc. 1960
    • (1960) Probability Theory
    • Loeve, M.1
  • 12
    • 0002173983 scopus 로고
    • Absence of self-averaging of the order parameter in the Sherrington-Kirkpatrick model
    • [P-S]
    • [P-S] Pastur, L., Shcherbina, M.: Absence of self-averaging of the order parameter in the Sherrington-Kirkpatrick model. J. Stat. Phys. 62, 1-26 (1991)
    • (1991) J. Stat. Phys. , vol.62 , pp. 1-26
    • Pastur, L.1    Shcherbina, M.2
  • 13
    • 21344485673 scopus 로고
    • The replica-symmetric solution without replica trick for the Hopfield model
    • [P-S-T1]
    • [P-S-T1] Pastur, L., Shcherbina, M., Tirozzi, B.: The replica-symmetric solution without replica trick for the Hopfield model. J. Stat. Phys. 74(5/6), 1161-1183 (1994)
    • (1994) J. Stat. Phys. , vol.74 , Issue.5-6 , pp. 1161-1183
    • Pastur, L.1    Shcherbina, M.2    Tirozzi, B.3
  • 14
    • 0033241160 scopus 로고    scopus 로고
    • On the replica symmetric equations for the Hopfield model
    • [P-S-T2]
    • [P-S-T2] Pastur, L., Shcherbina, M., Tirozzi, B.: On the replica symmetric equations for the Hopfield model. J. Math. Phys. 40 (1999)
    • (1999) J. Math. Phys. , vol.40
    • Pastur, L.1    Shcherbina, M.2    Tirozzi, B.3
  • 15
    • 0000862452 scopus 로고    scopus 로고
    • On the replica symmetric solution for the Sherrington-Kirkpatrick model
    • [S1]
    • [S1] Shcherbina, M.V.: On the replica symmetric solution for the Sherrington-Kirkpatrick model. Helvetica Physica Acta 70, 772-797 (1997)
    • (1997) Helvetica Physica Acta , vol.70 , pp. 772-797
    • Shcherbina, M.V.1
  • 16
    • 0012920324 scopus 로고    scopus 로고
    • Some estimates for the critical temperature of the Sherrington-Kirkpatrick model with magnetic field
    • [S2]. World Scientific, Singapore
    • [S2] Shcherbina, M.: Some estimates for the critical temperature of the Sherrington-Kirkpatrick model with magnetic field. In: Mathematical Results in Statistical Mechanics. World Scientific, Singapore, 1999, pp. 455-474
    • (1999) Mathematical Results in Statistical Mechanics , pp. 455-474
    • Shcherbina, M.1
  • 17
    • 21144472818 scopus 로고
    • The free energy of a class of Hopfield models
    • [S-T1]
    • [S-T1] Shcherbina, M., Tirozzi, B.: The free energy of a class of Hopfield models. J. Stat. Phys. 72(1/2), 113-125 (1993)
    • (1993) J. Stat. Phys. , vol.72 , Issue.1-2 , pp. 113-125
    • Shcherbina, M.1    Tirozzi, B.2
  • 18
    • 0038237350 scopus 로고    scopus 로고
    • On the volume of the intersection of a sphere with random half spaces
    • [S-T2]
    • [S-T2] Shcherbina, M., Tirozzi, B.: On the volume of the intersection of a sphere with random half spaces. C.R. Acad. Sci. Paris Ser. I 334, 1-4 (2002)
    • (2002) C.R. Acad. Sci. Paris Ser. I , vol.334 , pp. 1-4
    • Shcherbina, M.1    Tirozzi, B.2
  • 19
    • 0009148982 scopus 로고    scopus 로고
    • Rigorous results for the Hopfield model with many patterns
    • [T1]
    • [T1] Talagrand, M.: Rigorous results for the Hopfield model with many patterns. Prob. Theor. Rel. Fields 110, 176-277 (1998)
    • (1998) Prob. Theor. Rel. Fields , vol.110 , pp. 176-277
    • Talagrand, M.1
  • 20
    • 0034214576 scopus 로고    scopus 로고
    • Exponential inequalities and replica symmetry breaking for the Sherrington-Kirkpatrick model
    • [T2]
    • [T2] Talagrand, M.: Exponential inequalities and replica symmetry breaking for the Sherrington-Kirkpatrick model. Ann. Probab. 28, 1018-1068 (2000)
    • (2000) Ann. Probab. , vol.28 , pp. 1018-1068
    • Talagrand, M.1
  • 21
    • 0034345587 scopus 로고    scopus 로고
    • Intersecting random ralf-spaces: Toward the Gardner-Derrida problem
    • [T3]
    • [T3] Talagrand, M.: Intersecting random ralf-spaces: Toward the Gardner-Derrida problem. Ann. Probab. 28, 725-758 (2000)
    • (2000) Ann. Probab. , vol.28 , pp. 725-758
    • Talagrand, M.1
  • 22
    • 0033422085 scopus 로고    scopus 로고
    • Self averaging and the space of interactions in neural networks
    • [T4]
    • [T4] Talagrand, M.: Self averaging and the space of interactions in neural networks. Random Structures and Algorithms 14, 199-213 (1998)
    • (1998) Random Structures and Algorithms , vol.14 , pp. 199-213
    • Talagrand, M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.