Large Deviations for Langevin
نویسندگان
چکیده
We study the asymptotic behavior 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 measure Q 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 to Q in the case of a symmetric initial law and even potential for the free spin.
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