Source: Ann. Probab. Volume 25, Number 3
(1997), 1367-1422.
We study the asymptotic behavior of symmetric spin glass dynamics
in the Sherrington–Kirkpatrick model as proposed by
Sompolinsky–Zippelius. We prove that the averaged law of the empirical
measure on the path space of these dynamics satisfies a large deviation upper
bound in the high temperature regime. We study the rate function which governs
this large deviation upper bound and prove that it achieves its minimum value
at a unique probability measure $Q$ which is not Markovian. We deduce an
averaged and a quenched law of large numbers. We then study the evolution of
the Gibbs measure of a spin glass under Sompolinsky–Zippelius dynamics.
We also prove a large deviation upper bound for the law of the empirical
measure and describe the asymptotic behavior of a spin on path space under this
dynamic in the high temperature regime.
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