Large deviations for Langevin spin glass dynamics |
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Authors: | G B Arous A Guionnet |
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Institution: | (1) URA 762, CNRS, DMI, Ecole Normale Superieure, F-75230 Paris, France;(2) URA 743, CNRS, Université de Paris Sud, Bat. 425, F-91405 Orsay, France |
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Abstract: | Summary We study the asymptotic behaviour of asymmetrical spin glass dynamics in a Sherrington-Kirkpatrick model as proposed by Sompolinsky-Zippelius. We prove that the annealed law of the empirical measure on path space of these dynamics satisfy a large deviation principle in the high temperature regime. We study the rate function of this large deviation principle and prove that it achieves its minimum value at a unique probability measureQ which is not markovian. We deduce that the quenched law of the empirical measure converges to
Q
. Extending then the preceeding results to replicated dynamics, we investigate the quenched behavior of a single spin. We get quenched convergence toQ in the case of a symmetric initial law and even potential for the free spin. |
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Keywords: | 60F10 60H10 60K35 82C44 |
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