Abstract
The purpose of this note is to review and summarize recent results on dynamics of mean-field spin glasses.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Aizenman, M., Lebowitz, J.L, and Ruelle, D, Some rigorous results on the Sherrington-Kirkpatrick spin glass model, Commun. Math. Phys. 112, 3–20 (1987).
Barrat, A., thesis, Université Paris VI, Paris, France (1996).
Ben Arous, G., Guionnet, A., Large deviations for Langevin spin glass dynamics, Probab. Theor. Rel. Fields.
Ben Arous, G., Guionnet, A., Symmetric Langevin spin glass dynamics, accepted by Ann. Probab.
Cessac, B., thesis, Université Paul sabatier, Toulouse, France (1994).
Cesi, F., Maes, C., and Martinelli, F., Relaxation of disordered magnets in the Griffiths’ regime, preprint (1996).
Cesi, F., Maes, C., and Martinelli, F., Relaxation to equilibrium for two dimensional disordered Ising systems in the Griffiths phase, preprint (1996).
Comets, F., Neveu, J., Modèle de Sherrington-Kirkpatriek à haute temperature et calcul stochastique, preprint, Ecole Polytechnique.
Dawson, D.A., Gartner, J., Large déviations from the McKean-Vlasov limit for weakly interacting diffusions, Stochastics, 20, 247–308 (1987).
Deuschel, J-D. and Stroock, D.W., Large deviations, Academic Press.
Grunwald, M., Sanov results for Glauber spin-glass dynamics. Probab. Theor. Rel. Fields. 106 (2), 187–232.
Guionnet, A., Annealed and quenched propagation of chaos for Langevin spin glass dynamics, to appear in Probab. Theor. Rel. Fields.
Guionnet, A., and Zegarlinski, B., Decay to equilibrium in random spin Ssystems on a lattice, Commun. Math. Phys. 181 (3), 703–732 (1996).
Leonard, C., Diffusions avec interaction, Ann. Inst. Henri Poincaré 22, (2) 237–262 (1986).
Mezard, M., Parisi, G., and Virasoro, M., Spin glass theory and beyond, World Scientific, Lecture Notes in Physics, Singapore, 1987.
Neveu, J., Processus aléatoires Gaussiens, Presses de l’université de Montréal.
Revuz, D. and Yor M., Continuous martingales and Brownian motion, Springer, 1991.
Sompolinski, H. and Zippelius, A., Phys. Rev. Lett. 47 359 (1981).
Sznitman, A.-S., Equation de type Boltzmann spatialement homogenes Z.f. Wahrscheinlichkeitstheorie verw. Gebiete 66, 559–592 (1984).
Talagrand, M., Concentration of measure and isoperimetric inequalities in product space, Inst. Hautes Etudes Sci. Publ. Math 81, 73–208 (1995).
Tanaka, H., Limit theorems for certain diffusion processes, Proceedings of the Taniguchi Symp., Katata 1982, 469–488, Tokyo, Kinokuniya, 1984.
Zegarlinski, B., Strong decay to equilibrium in one dimensional random spin systems, J. Stat. Phys. 77, 717–732 (1994).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1998 Birkhäuser Boston
About this chapter
Cite this chapter
Arous, G.B., Guionnet, A. (1998). Langevin Dynamics for Sherrington-Kirkpatrick Spin Glasses. In: Bovier, A., Picco, P. (eds) Mathematical Aspects of Spin Glasses and Neural Networks. Progress in Probability, vol 41. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-4102-7_9
Download citation
DOI: https://doi.org/10.1007/978-1-4612-4102-7_9
Publisher Name: Birkhäuser Boston
Print ISBN: 978-1-4612-8653-0
Online ISBN: 978-1-4612-4102-7
eBook Packages: Springer Book Archive