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Lectures on Probability Theory and Statistics pp 269–283Cite as

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

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Bibliography

  1. M. Aizenman, J.L. Lebowitz, D. Ruelle, Some rigorous results on the Sherrington-Kirkpatrick model, Coramun. Math. Phys., 112 (1987) 3–20.

    Article  MATH  MathSciNet  Google Scholar 

  2. A. Bovier. P. Picco (editors), Mathematical Aspects of Spin Glasses and Neural Networks, Progress in Probability, Vol. 41, Birkhauser, Boston, 1997.

    Google Scholar 

  3. F. Comets, A spherical bound for the Sherrington-Kirkpatrick model, Hommage à P.-A. Meyer et J. Neveu, Astensque, 236, (1996) 103–108.

    MathSciNet  Google Scholar 

  4. 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.

    Article  MATH  MathSciNet  Google Scholar 

  5. B. Derrida, Random energy model: An exactly solvable model of disordered systems, Phys. Rev. B, 24, #5 (1981) 2613–2626.

    Article  MathSciNet  Google Scholar 

  6. J. Frohlich, B. Zegarlinski, Some comments on the Sherrington-Kirkpatrick model of spin glasses, Coramun. Math. Phys., 112 (1987) 553–566.

    Article  MathSciNet  Google Scholar 

  7. E. Gardner. Spin glasses with p-spin interactions, Nuclear Phys. B, 257, #6 (1985) 747–765.

    Article  MathSciNet  Google Scholar 

  8. 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.

    Article  MATH  MathSciNet  Google Scholar 

  9. 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. J.-P. Kahane, Une inegalite du type de Slepian et Gordon sur les processus gaussiens, Israel J. Math., 55, 1 (1986) 109–110.

    Article  MATH  MathSciNet  Google Scholar 

  11. J. Kosterlitz, D. Thouless, R. Jones, Spherical model of spin glass, Phys. Rev. Lett, 36 (1976) 1217–1220.

    Article  Google Scholar 

  12. M. Mezard, G. Parisi, M. Virasoro, Spin glass Theory and beyond, World Scientific, Singapore, 1987.

    MATH  Google Scholar 

  13. G. Parisi, Field Theory, Disorder, Simulation, World Scientific Lecture Notes in Physics 45, World Scientific, Singapore, 1992.

    Google Scholar 

  14. 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. J. Pitman, M. Yor, The two-parameter Poisson-Dirichlet distribution derived from a stable subordinator, Ann. Probab., 25 (1997) 855–900.

    Article  MATH  MathSciNet  Google Scholar 

  16. M. Shcherbina, On the replica-symmetric solution of the Sherrington-Kirkpatrick model, Helv. Phys. Ada, 70 (1997) 838–853.

    MATH  MathSciNet  Google Scholar 

  17. D. Sherrington, S. Kirkpatrick, Solvable model of spin glass, Phys. Rev. Lett., 35 (1972) 1792–1796.

    Article  Google Scholar 

  18. M. Talagrand, Concentration of measure and isoperimetric inequalities in product spaces, Publ. Math. I.H.E.S., 81 (1995) 73–205.

    MATH  MathSciNet  Google Scholar 

  19. —, The Sherrington-Kirkpatrick model: a challenge to mathematicians, Probab. Theory Related Fields, 110 (1998) 109–176.

    Article  MATH  MathSciNet  Google Scholar 

  20. —, Rigorous low temperature results for the p-spin interaction model, Probab. Theory Related Fields, 117 (2000) 303–360.

    Article  MATH  MathSciNet  Google Scholar 

  21. —, Exponential inequalities and replica-symmetry breaking for the Sherrington-Kirkpatrick model, Ann. Probab., 28 (2000) 1018–1062.

    Article  MATH  MathSciNet  Google Scholar 

  22. —, 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. —, Verres de spin et optimisation combinatoire, Séminaire Bourbaki, March 1999,Asterisque, 266 (2000) Exp. n° 859, 287–317.

    Google Scholar 

  24. —, Self organization in a spin glass model, in preparation.

    Google Scholar 

  25. —, On the high temperature region of the Sherrington-Kirkpatrick model, Ann. Probab., to appear.

    Google Scholar 

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Editor information

Editors and Affiliations

  1. Institute for Applied Mathematics, Probability Theory and Statistics, University of Bonn, Wegelerstr. 6, 53115, Bonn, Germany

    Sergio Albeverio

  2. Department of Financial and Actuarial Mathematics, Vienna University of Technology, Wiedner Hauptstraße 8-10/105, 1040, Vienna, Austria

    Walter Schachermayer

  3. Equipe d’Analyse, Université Paris VI, 4 Place Jussieu, 75230, Paris Cedex 05, France

    Michel Talagrand

  4. Laboratoire de Mathématiques Appliquées UMR CNRS 6620, Université Blaise Pascal, 63177, Aubière Cedex, Clermont-Ferrand, France

    Pierre Bernard

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(2003). Emergence and separation of the lumps in the p-spin interaction model. In: Albeverio, S., Schachermayer, W., Talagrand, M., Bernard, P. (eds) Lectures on Probability Theory and Statistics. Lecture Notes in Mathematics, vol 1816. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44922-1_19

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  • DOI: https://doi.org/10.1007/3-540-44922-1_19

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40335-7

  • Online ISBN: 978-3-540-44922-5

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