Emergence and separation of the lumps in the p-spin interaction model

Part of the Lecture Notes in Mathematics book series (LNM, volume 1816)


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  1. [A-L-R]
    M. Aizenman, J.L. Lebowitz, D. Ruelle, Some rigorous results on the Sherrington-Kirkpatrick model, Coramun. Math. Phys., 112 (1987) 3–20.zbMATHCrossRefMathSciNetGoogle Scholar
  2. [B-P]
    A. Bovier. P. Picco (editors), Mathematical Aspects of Spin Glasses and Neural Networks, Progress in Probability, Vol. 41, Birkhauser, Boston, 1997.Google Scholar
  3. [C]
    F. Comets, A spherical bound for the Sherrington-Kirkpatrick model, Hommage à P.-A. Meyer et J. Neveu, Astensque, 236, (1996) 103–108.MathSciNetGoogle Scholar
  4. [C-N]
    F. Comets, J. Neveu, The Sherrington-Kirkpatrick model of spin glasses and stochastic calculus: the high temperature case, Comm. Math. Phys., 166, 3 (1995) 549–564.zbMATHCrossRefMathSciNetGoogle Scholar
  5. [D]
    B. Derrida, Random energy model: An exactly solvable model of disordered systems, Phys. Rev. B, 24, #5 (1981) 2613–2626.CrossRefMathSciNetGoogle Scholar
  6. [F-Z]
    J. Frohlich, B. Zegarlinski, Some comments on the Sherrington-Kirkpatrick model of spin glasses, Coramun. Math. Phys., 112 (1987) 553–566.CrossRefMathSciNetGoogle Scholar
  7. [G]
    E. Gardner. Spin glasses with p-spin interactions, Nuclear Phys. B, 257, #6 (1985) 747–765.CrossRefMathSciNetGoogle Scholar
  8. [G-G]
    S. Ghirlanda, F. Gucrra, General properties of overlap probability distributions in disordered spin systems. Towards Parisi ultrametiicity, J. Phys. A, 31, #46 (1998) 9149–9155.zbMATHCrossRefMathSciNetGoogle Scholar
  9. [I-S-T]
    I.A. Ibragimov, V. Sudakov, B.S. Tsirelson, Norms of Gaussian sample functions, “Proceedings of the Third Japan-USSR Symposium on Probability”, Tashkent, 1975, Lecture Notes in Math., 550, Springer Verlag, Berlin, 1976, 20–41.Google Scholar
  10. [K]
    J.-P. Kahane, Une inegalite du type de Slepian et Gordon sur les processus gaussiens, Israel J. Math., 55, 1 (1986) 109–110.zbMATHCrossRefMathSciNetGoogle Scholar
  11. [K-T-J]
    J. Kosterlitz, D. Thouless, R. Jones, Spherical model of spin glass, Phys. Rev. Lett, 36 (1976) 1217–1220.CrossRefGoogle Scholar
  12. [M-P-V]
    M. Mezard, G. Parisi, M. Virasoro, Spin glass Theory and beyond, World Scientific, Singapore, 1987.zbMATHGoogle Scholar
  13. [P]
    G. Parisi, Field Theory, Disorder, Simulation, World Scientific Lecture Notes in Physics 45, World Scientific, Singapore, 1992.Google Scholar
  14. [Pi]
    G. Pisier, Probabilistic methods in the geometry of Banach Spaces, Probability and analysis, Varenna 1985, Springer Verlag Lecture Notes in Math. n° 1206 (1996) 167–241.Google Scholar
  15. [P-Y]
    J. Pitman, M. Yor, The two-parameter Poisson-Dirichlet distribution derived from a stable subordinator, Ann. Probab., 25 (1997) 855–900.zbMATHCrossRefMathSciNetGoogle Scholar
  16. [Sh]
    M. Shcherbina, On the replica-symmetric solution of the Sherrington-Kirkpatrick model, Helv. Phys. Ada, 70 (1997) 838–853.zbMATHMathSciNetGoogle Scholar
  17. [S-K]
    D. Sherrington, S. Kirkpatrick, Solvable model of spin glass, Phys. Rev. Lett., 35 (1972) 1792–1796.CrossRefGoogle Scholar
  18. [Tl]
    M. Talagrand, Concentration of measure and isoperimetric inequalities in product spaces, Publ. Math. I.H.E.S., 81 (1995) 73–205.zbMATHMathSciNetGoogle Scholar
  19. [T2]
    —, The Sherrington-Kirkpatrick model: a challenge to mathematicians, Probab. Theory Related Fields, 110 (1998) 109–176.zbMATHCrossRefMathSciNetGoogle Scholar
  20. [T3]
    —, Rigorous low temperature results for the p-spin interaction model, Probab. Theory Related Fields, 117 (2000) 303–360.zbMATHCrossRefMathSciNetGoogle Scholar
  21. [T4]
    —, Exponential inequalities and replica-symmetry breaking for the Sherrington-Kirkpatrick model, Ann. Probab., 28 (2000) 1018–1062.zbMATHCrossRefMathSciNetGoogle Scholar
  22. [T5]
    —, Huge random structures and mean field models for spin glasses, in “Proceedings of the International Congress of Mathematicians, Vol. I (Berlin 1998)“, Documenta Math., Extra Vol. I (1998) 507–536.Google Scholar
  23. [T6]
    —, Verres de spin et optimisation combinatoire, Séminaire Bourbaki, March 1999,Asterisque, 266 (2000) Exp. n° 859, 287–317.Google Scholar
  24. [T7]
    —, Self organization in a spin glass model, in preparation.Google Scholar
  25. [T8]
    —, On the high temperature region of the Sherrington-Kirkpatrick model, Ann. Probab., to appear.Google Scholar

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