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Volumn 40, Issue 4, 2004, Pages 439-480

Derrida's Generalised Random Energy Models 1: Models with finitely many hierarchies

Author keywords

Extreme values; Gaussian processes; Generalised random energy model; Ghirlanda Guerra identities; Order statistics; Poisson cascades; Spin glasses

Indexed keywords


EID: 2942556515     PISSN: 02460203     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.anihpb.2003.09.002     Document Type: Article
Times cited : (96)

References (36)
  • 1
    • 0032165110 scopus 로고    scopus 로고
    • On the stability of the quenched state in mean field spin-glass models
    • Aizenmann M. Contucci P. On the stability of the quenched state in mean field spin-glass models J. Statist. Phys. 92 1998 765-783
    • (1998) J. Statist. Phys. , vol.92 , pp. 765-783
    • Aizenmann, M.1    Contucci, P.2
  • 2
    • 0010294155 scopus 로고    scopus 로고
    • Statistical Mechanics of Disordered Systems
    • Aarhus
    • Bovier A. Statistical Mechanics of Disordered Systems MaPhySto Lecture Notes vol. 10 2001 Aarhus
    • (2001) MaPhySto Lecture Notes , vol.10
    • Bovier, A.1
  • 3
    • 0004340648 scopus 로고    scopus 로고
    • The Hopfield model as a generalised random mean field model
    • A. Bovier, & P. Picco (Eds.), Boston: Birkhäuser
    • Bovier A. Gayrard V. The Hopfield model as a generalised random mean field model in: Bovier A. Picco P. (Eds.), Mathematics of Spin Glasses and Neural Networks Progress in Probablity 1997 Birkhäuser Boston
    • (1997) Mathematics of Spin Glasses and Neural Networks
    • Bovier, A.1    Gayrard, V.2
  • 4
    • 2942539477 scopus 로고    scopus 로고
    • Derrida's generalised random energy models 2. Models with continuous hierarchies
    • Submitted for publication
    • A. Bovier, I. Kurkova, Derrida's generalised random energy models 2. Models with continuous hierarchies, Ann. IHP (2002), submitted for publication
    • (2002) Ann. IHP
    • Bovier, A.1    Kurkova, I.2
  • 5
    • 2942599867 scopus 로고    scopus 로고
    • Gibbs measures of Derrida's generalised random energy models and geneologies of Neveu's continuous state branching process
    • Submitted for publication
    • A. Bovier, I. Kurkova, Gibbs measures of Derrida's generalised random energy models and geneologies of Neveu's continuous state branching process, Probab. Theor. Relat. Fields (2003), submitted for publication
    • (2003) Probab. Theor. Relat. Fields
    • Bovier, A.1    Kurkova, I.2
  • 6
    • 0036018190 scopus 로고    scopus 로고
    • Fluctuations of the free energy in the REM and the p-spin SK-models
    • Bovier A. Kurkova I. Löwe M. Fluctuations of the free energy in the REM and the p-spin SK-models Ann. Probab. 30 2002 605-651
    • (2002) Ann. Probab. , vol.30 , pp. 605-651
    • Bovier, A.1    Kurkova, I.2    Löwe, M.3
  • 7
    • 84980189802 scopus 로고
    • Maximal displacement of branching Brownian motion
    • Bramson M.D. Maximal displacement of branching Brownian motion Comm. Pure Appl. Math. 31 1978 531-581
    • (1978) Comm. Pure Appl. Math. , vol.31 , pp. 531-581
    • Bramson, M.D.1
  • 8
    • 0011409893 scopus 로고
    • On the existence of thermodynamics for the generalised random energy model
    • Capocaccia D. Cassandro M. Picco P. On the existence of thermodynamics for the generalised random energy model J. Statist. Phys. 46 1987 493-505
    • (1987) J. Statist. Phys. , vol.46 , pp. 493-505
    • Capocaccia, D.1    Cassandro, M.2    Picco, P.3
  • 9
    • 35949021286 scopus 로고
    • Random energy model: Limit of a family of disordered models
    • Derrida B. Random energy model: limit of a family of disordered models Phys. Rev. Lett. 45 1980 79-82
    • (1980) Phys. Rev. Lett. , vol.45 , pp. 79-82
    • Derrida, B.1
  • 10
    • 4243861085 scopus 로고
    • Random energy model: An exactly solvable model of disordered systems
    • Derrida B. Random energy model: an exactly solvable model of disordered systems Phys. Rev. B 24 1981 2613-2626
    • (1981) Phys. Rev. B , vol.24 , pp. 2613-2626
    • Derrida, B.1
  • 11
    • 0000843415 scopus 로고
    • A generalisation of the random energy model that includes correlations between the energies
    • Derrida B. A generalisation of the random energy model that includes correlations between the energies J. Phys. Lett. 46 1985 401-407
    • (1985) J. Phys. Lett. , vol.46 , pp. 401-407
    • Derrida, B.1
  • 12
    • 20444430048 scopus 로고
    • Solution of the generalised random energy model
    • Derrida B. Gardner E. Solution of the generalised random energy model J. Phys. C 19 1986 2253-2274
    • (1986) J. Phys. C , vol.19 , pp. 2253-2274
    • Derrida, B.1    Gardner, E.2
  • 13
    • 0000996412 scopus 로고
    • Magnetic properties and function q(x) of the generalised random energy model
    • Derrida B. Gardner E. Magnetic properties and function q(x) of the generalised random energy model J. Phys. C 19 1986 5783-5798
    • (1986) J. Phys. C , vol.19 , pp. 5783-5798
    • Derrida, B.1    Gardner, E.2
  • 14
    • 0003099623 scopus 로고
    • The probability distribution of the partition function of the random energy model
    • Gardner E. Derrida B. The probability distribution of the partition function of the random energy model J. Phys. A 22 1989 1975-1981
    • (1989) J. Phys. A , vol.22 , pp. 1975-1981
    • Gardner, E.1    Derrida, B.2
  • 17
    • 0001588819 scopus 로고
    • On a third order phase transition
    • Eisele T.H. On a third order phase transition Comm. Math. Phys. 90 1983 125-159
    • (1983) Comm. Math. Phys. , vol.90 , pp. 125-159
    • Eisele, T.H.1
  • 19
    • 0032553281 scopus 로고    scopus 로고
    • General properties of the overlap probability distributions in disordered spin systems. Towards Parisi ultrametricity
    • Ghirlanda S. Guerra F. General properties of the overlap probability distributions in disordered spin systems. Towards Parisi ultrametricity J. Phys. A 31 1998 9144-9155
    • (1998) J. Phys. A , vol.31 , pp. 9144-9155
    • Ghirlanda, S.1    Guerra, F.2
  • 20
    • 0000518213 scopus 로고
    • Fluctuations in Derrida's random energy and generalised random energy models
    • Galvez A. Martinez S. Picco P. Fluctuations in Derrida's random energy and generalised random energy models J. Statist. Phys. 54 1989 515-529
    • (1989) J. Statist. Phys. , vol.54 , pp. 515-529
    • Galvez, A.1    Martinez, S.2    Picco, P.3
  • 21
    • 0004212801 scopus 로고
    • Fourth ed. Berlin: Akademie Verlag
    • Kallenberg O. Random Measures fourth ed. 1986 Akademie Verlag Berlin
    • (1986) Random Measures
    • Kallenberg, O.1
  • 22
    • 2942628806 scopus 로고    scopus 로고
    • On a representation of Gibbs measure for R.E.M
    • preprint Samos 151
    • M.F. Kratz, P. Picco, On a representation of Gibbs measure for R.E.M., preprint Samos 151, 2002
    • (2002)
    • Kratz, M.F.1    Picco, P.2
  • 23
    • 0037276762 scopus 로고    scopus 로고
    • Temperature dependence of the Gibbs State in the random energy model
    • Kurkova I. Temperature dependence of the Gibbs State in the random energy model J. Stat. Phys. 111 1/2 2003 35-56
    • (2003) J. Stat. Phys. , vol.111 , Issue.1-2 , pp. 35-56
    • Kurkova, I.1
  • 24
    • 0003910552 scopus 로고
    • Extremes and Related Properties of Random Sequences and Processes
    • Berlin: Springer
    • Leadbetter M.R. Lindgren G. Rootzén H. Extremes and Related Properties of Random Sequences and Processes 1983 Springer Berlin
    • (1983)
    • Leadbetter, M.R.1    Lindgren, G.2    Rootzén, H.3
  • 26
    • 0038056172 scopus 로고
    • A continuous state branching process in relation with the GREM model of spin glass theory
    • Rapport interne no 267, École Polytechnique
    • J. Neveu, A continuous state branching process in relation with the GREM model of spin glass theory, Rapport interne no 267, École Polytechnique, 1992
    • (1992)
    • Neveu, J.1
  • 27
    • 0001132742 scopus 로고
    • On the existence of thermodynamics for the random energy model
    • Olivieri E. Picco P. On the existence of thermodynamics for the random energy model Comm. Math. Phys. 96 1991 125-144
    • (1991) Comm. Math. Phys. , vol.96 , pp. 125-144
    • Olivieri, E.1    Picco, P.2
  • 29
    • 0004267646 scopus 로고
    • Princeton, NJ: Princeton University Press
    • Rockafellar R.T. Convex Analysis 1970 Princeton University Press Princeton, NJ
    • (1970) Convex Analysis
    • Rockafellar, R.T.1
  • 30
    • 0000545781 scopus 로고
    • A mathematical reformulation of Derrida's REM and GREM
    • Ruelle D. A mathematical reformulation of Derrida's REM and GREM Comm. Math. Phys. 108 1987 225-239
    • (1987) Comm. Math. Phys. , vol.108 , pp. 225-239
    • Ruelle, D.1
  • 32
    • 51249165477 scopus 로고
    • Concentration of measure and isoperimetric inequalities in product space
    • Talagrand M. Concentration of measure and isoperimetric inequalities in product space Publ. Math. IHES 81 1995 73-205
    • (1995) Publ. Math. IHES , vol.81 , pp. 73-205
    • Talagrand, M.1
  • 33
    • 0009148982 scopus 로고    scopus 로고
    • Rigorous results for the Hopfield model with many patterns
    • Talagrand M. Rigorous results for the Hopfield model with many patterns Probab. Theory Related Fields 110 1998 177-276
    • (1998) Probab. Theory Related Fields , vol.110 , pp. 177-276
    • Talagrand, M.1
  • 34
    • 0004032969 scopus 로고    scopus 로고
    • Mean Field Models for Spin Glasses: A First Course
    • Lecture Notes of the École des Probabilités de St. Flour Springer, submitted for publication
    • M. Talagrand, Mean Field Models for Spin Glasses: a First Course, Lecture Notes of the 2000 École des Probabilités de St. Flour, Lecture Notes in Mathematics, Springer, submitted for publication
    • (2000) Lecture Notes in Mathematics
    • Talagrand, M.1
  • 35
    • 0037340681 scopus 로고    scopus 로고
    • Self organisation in the low-temperature region of a spin glass model
    • Talagrand M. Self organisation in the low-temperature region of a spin glass model Rev. Math. Phys. 15 2003 1-78
    • (2003) Rev. Math. Phys. , vol.15 , pp. 1-78
    • Talagrand, M.1


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