@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},
pages = {481--495},
year = {2004},
publisher = {Elsevier},
volume = {40},
number = {4},
doi = {10.1016/j.anihpb.2003.09.003},
mrnumber = {2070335},
zbl = {1121.82021},
language = {en},
url = {https://www.numdam.org/articles/10.1016/j.anihpb.2003.09.003/}
}
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 SP - 481 EP - 495 VL - 40 IS - 4 PB - Elsevier UR - https://www.numdam.org/articles/10.1016/j.anihpb.2003.09.003/ DO - 10.1016/j.anihpb.2003.09.003 LA - en ID - AIHPB_2004__40_4_481_0 ER -
%0 Journal Article %A Bovier, Anton %A Kurkova, Irina %T Derrida's generalized random energy models 2 : models with continuous hierarchies %J Annales de l'I.H.P. Probabilités et statistiques %D 2004 %P 481-495 %V 40 %N 4 %I Elsevier %U https://www.numdam.org/articles/10.1016/j.anihpb.2003.09.003/ %R 10.1016/j.anihpb.2003.09.003 %G en %F 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) no. 4, pp. 481-495. doi: 10.1016/j.anihpb.2003.09.003
[1] , , On the stability of the quenched state in mean field spin-glass models, J. Statist. Phys. 92 (1998) 765-783. | Zbl | MR
[2] , , Rounding effects of quenched randomness on first-order phase transitions, Comm. Math. Phys. 130 (1990) 489-528. | Zbl | MR
[3] , , , An extended variational principle for the SK spin-glass model, preprint , cond-mat/0306386.
[4] , , The Bolthausen-Snitzman coalescent and the genealogy of continuous state branching processes, Probab. Theory Related Fields 117 (2000) 249-266. | Zbl
[5] , , , Entropic repulsion and the maximum of the two-dimensional harmonic crystal, Ann. Probab. 29 (2001) 1670-1692. | Zbl | MR
[6] , , On Ruelle's probability cascades and an abstract cavity method, Comm. Math. Phys. 107 (1998) 247-276. | Zbl
[7] , , Derrida's Generalized Random Energy models 1. Models with finitely many hierarchies, Ann. Inst. H. Poincaré (2004). | Zbl | Numdam
[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] , , The Hopfield model as a generalized random mean field model, in: , (Eds.), Mathematics of Spin Glasses and Neural Networks, Progress in Probability, Birkhäuser, Boston, 1997. | Zbl
[10] , Maximal displacement of branching Brownian motion, Comm. Pure Appl. Math. 31 (1978) 531-581. | Zbl | MR
[11] , , , On the existence of thermodynamics for the Generalised Random Energy Model, J. Stat. Phys. 46 (1987) 493-505. | MR
[12] , A generalization of the random energy model that includes correlations between the energies, J. Phys. Lett. 46 (1985) 401-407.
[13] , , Solution of the generalized random energy model, J. Phys. C 19 (1986) 2253-2274.
[14] , , Magnetic properties and function q(x) of the generalised random energy model, J. Phys. C 19 (1986) 5783-5798.
[15] , , The probability distribution of the partition function of the random energy model, J. Phys. A 22 (1989) 1975-1981. | MR
[16] , , General properties of the overlap probability distributions in disordered spin systems. Towards Parisi ultrametricity, J. Phys. A 31 (1998) 9144-9155. | Zbl | MR
[17] F. Guerra, Broken replica symmetry bounds in the mean field spin glass model, preprint, 2002. | MR
[18] , , The thermodynamics limit in mean field spin glass models, Comm. Math. Phys. (2002), submitted for publication. | Zbl | MR
[19] , , , Extremes and Related Properties of Random Sequences and Processes, Springer, Berlin, 1983. | Zbl | MR
[20] , , Probability in Banach Space, Springer, Berlin, 1991. | Zbl | MR
[21] , Topics in Disordered Systems, Lectures in Mathematics ETH Zürich, Birkhäuser, Basel, 1997. | Zbl | MR
[22] , , Thermodynamic chaos and the structure of short range spin glasses, in: , (Eds.), Mathematical Aspects of Spin Glasses and Neural Networks, Progress in Probability, Birkhäuser, Boston, 1997. | Zbl | MR
[23] , , Metastate approach to thermodynamic chaos, Phys. Rev. E 55 (1997) 5194-5211. | MR
[24] , Convex Analysis, Princeton University Press, Princeton, NJ, 1970. | Zbl | MR
[25] , A mathematical reformulation of Derrida's REM and GREM, Comm. Math. Phys. 108 (1987) 225-239. | Zbl | MR
[26] , , Solvable model of a spin glass, Phys. Rev. Lett. 35 (1972) 1792-1796.
[27] , Rigorous low temperature results for mean field p-spin interaction models, Probab. Theory Related Fields 117 (2000) 303-360. | Zbl | MR
[28] M. Talagrand, Self organization in the low-temperature region of a spin glass model, preprint, 2002. | MR
[29] , Rigorous results for the Hopfield model with many patterns, Probab. Theory Related Fields 110 (1998) 177-276. | Zbl | MR
[30] , Spin Glasses: a Challenge to Mathematicians, Ergebnisse der Mathematik und ihrer Grenzgebiete, vol. 46, Springer, Berlin, 2003. | Zbl | MR
Cité par Sources :






