Derrida's generalized random energy models 2 : models with continuous hierarchies
Bovier, Anton ; Kurkova, Irina
Annales de l'I.H.P. Probabilités et statistiques, Tome 40 (2004), p. 481-495 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@article{AIHPB_2004__40_4_481_0,
     author = {Bovier, Anton and Kurkova, Irina},
     title = {Derrida's generalized random energy models 2 : models with continuous hierarchies},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     volume = {40},
     year = {2004},
     pages = {481-495},
     doi = {10.1016/j.anihpb.2003.09.003},
     mrnumber = {2070335},
     zbl = {02081289},
     zbl = {1121.82021},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPB_2004__40_4_481_0}
}

Bovier, Anton; Kurkova, Irina. Derrida's generalized random energy models 2 : models with continuous hierarchies. Annales de l'I.H.P. Probabilités et statistiques, Tome 40 (2004) pp. 481-495. doi : 10.1016/j.anihpb.2003.09.003. http://gdmltest.u-ga.fr/item/AIHPB_2004__40_4_481_0/

[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. | MR 1657840 | Zbl 0963.82045

[2] M Aizenman, J Wehr, Rounding effects of quenched randomness on first-order phase transitions, Comm. Math. Phys. 130 (1990) 489-528. | MR 1060388 | Zbl 0714.60090

[3] M Aizenman, R Sims, S.L Starr, An extended variational principle for the SK spin-glass model, preprint , cond-mat/0306386.

[4] J Bertoin, J.F Le Gall, The Bolthausen-Snitzman coalescent and the genealogy of continuous state branching processes, Probab. Theory Related Fields 117 (2000) 249-266. | Zbl 0963.60086

[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. | MR 1880237 | Zbl 1034.82018

[6] E Bolthausen, A.-S Snitzman, On Ruelle's probability cascades and an abstract cavity method, Comm. Math. Phys. 107 (1998) 247-276. | Zbl 0927.60071

[7] A Bovier, I Kurkova, Derrida's Generalized Random Energy models 1. Models with finitely many hierarchies, Ann. Inst. H. Poincaré (2004). | Numdam | Zbl 02081288

[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] 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. | Zbl 0899.60087

[10] M.D Bramson, Maximal displacement of branching Brownian motion, Comm. Pure Appl. Math. 31 (1978) 531-581. | MR 494541 | Zbl 0361.60052

[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. | MR 883541

[12] B Derrida, A generalization of the random energy model that includes correlations between the energies, J. Phys. Lett. 46 (1985) 401-407.

[13] B Derrida, E Gardner, Solution of the generalized random energy model, J. Phys. C 19 (1986) 2253-2274.

[14] B Derrida, E Gardner, Magnetic properties and function q(x) of the generalised random energy model, J. Phys. C 19 (1986) 5783-5798.

[15] E Gardner, B Derrida, The probability distribution of the partition function of the random energy model, J. Phys. A 22 (1989) 1975-1981. | MR 1004905

[16] S Ghirlanda, F Guerra, General properties of the overlap probability distributions in disordered spin systems. Towards Parisi ultrametricity, J. Phys. A 31 (1998) 9144-9155. | MR 1662161 | Zbl 0953.82037

[17] F. Guerra, Broken replica symmetry bounds in the mean field spin glass model, preprint, 2002. | MR 1957729

[18] F Guerra, F Toninelli, The thermodynamics limit in mean field spin glass models, Comm. Math. Phys. (2002), submitted for publication. | MR 1930572 | Zbl 1004.82004

[19] M.R Leadbetter, G Lindgren, H Rootzén, Extremes and Related Properties of Random Sequences and Processes, Springer, Berlin, 1983. | MR 691492 | Zbl 0518.60021

[20] M Ledoux, L Talagrand, Probability in Banach Space, Springer, Berlin, 1991. | MR 1102015 | Zbl 0748.60004

[21] Ch.M Newman, Topics in Disordered Systems, Lectures in Mathematics ETH Zürich, Birkhäuser, Basel, 1997. | MR 1480664 | Zbl 0897.60093

[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. | MR 1601751 | Zbl 0896.60078

[23] C.M Newman, D.L Stein, Metastate approach to thermodynamic chaos, Phys. Rev. E 55 (1997) 5194-5211. | MR 1448389

[24] R.T Rockafellar, Convex Analysis, Princeton University Press, Princeton, NJ, 1970. | MR 274683 | Zbl 0193.18401

[25] D Ruelle, A mathematical reformulation of Derrida's REM and GREM, Comm. Math. Phys. 108 (1987) 225-239. | MR 875300 | Zbl 0617.60100

[26] D Sherrington, S Kirkpatrick, Solvable model of a spin glass, Phys. Rev. Lett. 35 (1972) 1792-1796.

[27] M Talagrand, Rigorous low temperature results for mean field p-spin interaction models, Probab. Theory Related Fields 117 (2000) 303-360. | MR 1774067 | Zbl 1016.82021

[28] M. Talagrand, Self organization in the low-temperature region of a spin glass model, preprint, 2002. | MR 1961185

[29] M Talagrand, Rigorous results for the Hopfield model with many patterns, Probab. Theory Related Fields 110 (1998) 177-276. | MR 1609015 | Zbl 0897.60041

[30] M Talagrand, Spin Glasses: a Challenge to Mathematicians, Ergebnisse der Mathematik und ihrer Grenzgebiete, vol. 46, Springer, Berlin, 2003. | MR 1993891 | Zbl 1033.82002