Derrida's generalized random energy models 2 : models with continuous hierarchies

Anton Bovier; Irina Kurkova

Annales de l'I.H.P. Probabilités et statistiques (2004)

  • Volume: 40, Issue: 4, page 481-495
  • ISSN: 0246-0203

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Bovier, Anton, and Kurkova, Irina. "Derrida's generalized random energy models 2 : models with continuous hierarchies." Annales de l'I.H.P. Probabilités et statistiques 40.4 (2004): 481-495. <http://eudml.org/doc/77820>.

@article{Bovier2004,
author = {Bovier, Anton, Kurkova, Irina},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {Gaussian processes; Generalized random energy model; Continuous hierarchies; Spin glasses; Poisson cascades; Probability cascades; Ghirlanda–Guerra identities},
language = {eng},
number = {4},
pages = {481-495},
publisher = {Elsevier},
title = {Derrida's generalized random energy models 2 : models with continuous hierarchies},
url = {http://eudml.org/doc/77820},
volume = {40},
year = {2004},
}

TY - JOUR
AU - Bovier, Anton
AU - Kurkova, Irina
TI - Derrida's generalized random energy models 2 : models with continuous hierarchies
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2004
PB - Elsevier
VL - 40
IS - 4
SP - 481
EP - 495
LA - eng
KW - Gaussian processes; Generalized random energy model; Continuous hierarchies; Spin glasses; Poisson cascades; Probability cascades; Ghirlanda–Guerra identities
UR - http://eudml.org/doc/77820
ER -

References

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  1. [1] M Aizenman, P Contucci, On the stability of the quenched state in mean field spin-glass models, J. Statist. Phys.92 (1998) 765-783. Zbl0963.82045MR1657840
  2. [2] M Aizenman, J Wehr, Rounding effects of quenched randomness on first-order phase transitions, Comm. Math. Phys.130 (1990) 489-528. Zbl0714.60090MR1060388
  3. [3] M Aizenman, R Sims, S.L Starr, An extended variational principle for the SK spin-glass model, preprint , cond-mat/0306386. 
  4. [4] J Bertoin, J.F Le Gall, The Bolthausen–Snitzman coalescent and the genealogy of continuous state branching processes, Probab. Theory Related Fields117 (2000) 249-266. Zbl0963.60086
  5. [5] E Bolthausen, J.-D Deuschel, G Giacomin, Entropic repulsion and the maximum of the two-dimensional harmonic crystal, Ann. Probab.29 (2001) 1670-1692. Zbl1034.82018MR1880237
  6. [6] E Bolthausen, A.-S Snitzman, On Ruelle's probability cascades and an abstract cavity method, Comm. Math. Phys.107 (1998) 247-276. Zbl0927.60071
  7. [7] A Bovier, I Kurkova, Derrida's Generalized Random Energy models 1. Models with finitely many hierarchies, Ann. Inst. H. Poincaré (2004). Zbl1121.82020
  8. [8] A. Bovier, I. Kurkova, Gibbs measures of Derrida's generalised random energy models and Geneologies of Neveu's continuous state branching process, Probab. Theory Related Fields (2003), submitted for publication. 
  9. [9] A Bovier, V Gayrard, The Hopfield model as a generalized random mean field model, in: Bovier A, Picco P (Eds.), Mathematics of Spin Glasses and Neural Networks, Progress in Probability, Birkhäuser, Boston, 1997. Zbl0899.60087
  10. [10] M.D Bramson, Maximal displacement of branching Brownian motion, Comm. Pure Appl. Math.31 (1978) 531-581. Zbl0361.60052MR494541
  11. [11] D Capocaccia, M Cassandro, P Picco, On the existence of thermodynamics for the Generalised Random Energy Model, J. Stat. Phys.46 (1987) 493-505. MR883541
  12. [12] B Derrida, A generalization of the random energy model that includes correlations between the energies, J. Phys. Lett.46 (1985) 401-407. 
  13. [13] B Derrida, E Gardner, Solution of the generalized random energy model, J. Phys. C19 (1986) 2253-2274. 
  14. [14] B Derrida, E Gardner, Magnetic properties and function q(x) of the generalised random energy model, J. Phys. C19 (1986) 5783-5798. 
  15. [15] E Gardner, B Derrida, The probability distribution of the partition function of the random energy model, J. Phys. A22 (1989) 1975-1981. MR1004905
  16. [16] S Ghirlanda, F Guerra, General properties of the overlap probability distributions in disordered spin systems. Towards Parisi ultrametricity, J. Phys. A31 (1998) 9144-9155. Zbl0953.82037MR1662161
  17. [17] F. Guerra, Broken replica symmetry bounds in the mean field spin glass model, preprint, 2002. MR1957729
  18. [18] F Guerra, F Toninelli, The thermodynamics limit in mean field spin glass models, Comm. Math. Phys. (2002), submitted for publication. Zbl1004.82004MR1930572
  19. [19] M.R Leadbetter, G Lindgren, H Rootzén, Extremes and Related Properties of Random Sequences and Processes, Springer, Berlin, 1983. Zbl0518.60021MR691492
  20. [20] M Ledoux, L Talagrand, Probability in Banach Space, Springer, Berlin, 1991. Zbl0748.60004MR1102015
  21. [21] Ch.M Newman, Topics in Disordered Systems, Lectures in Mathematics ETH Zürich, Birkhäuser, Basel, 1997. Zbl0897.60093MR1480664
  22. [22] Ch.M Newman, D.L Stein, Thermodynamic chaos and the structure of short range spin glasses, in: Bovier A, Picco P (Eds.), Mathematical Aspects of Spin Glasses and Neural Networks, Progress in Probability, Birkhäuser, Boston, 1997. Zbl0896.60078MR1601751
  23. [23] C.M Newman, D.L Stein, Metastate approach to thermodynamic chaos, Phys. Rev. E55 (1997) 5194-5211. MR1448389
  24. [24] R.T Rockafellar, Convex Analysis, Princeton University Press, Princeton, NJ, 1970. Zbl0193.18401MR274683
  25. [25] D Ruelle, A mathematical reformulation of Derrida's REM and GREM, Comm. Math. Phys.108 (1987) 225-239. Zbl0617.60100MR875300
  26. [26] D Sherrington, S Kirkpatrick, Solvable model of a spin glass, Phys. Rev. Lett.35 (1972) 1792-1796. 
  27. [27] M Talagrand, Rigorous low temperature results for mean field p-spin interaction models, Probab. Theory Related Fields117 (2000) 303-360. Zbl1016.82021MR1774067
  28. [28] M. Talagrand, Self organization in the low-temperature region of a spin glass model, preprint, 2002. MR1961185
  29. [29] M Talagrand, Rigorous results for the Hopfield model with many patterns, Probab. Theory Related Fields110 (1998) 177-276. Zbl0897.60041MR1609015
  30. [30] M Talagrand, Spin Glasses: a Challenge to Mathematicians, Ergebnisse der Mathematik und ihrer Grenzgebiete, vol. 46, Springer, Berlin, 2003. Zbl1033.82002MR1993891

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