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July 1997 Symmetric Langevin spin glass dynamics
G. Ben Arous, A. Guionnet
Ann. Probab. 25(3): 1367-1422 (July 1997). DOI: 10.1214/aop/1024404517


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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G. Ben Arous. A. Guionnet. "Symmetric Langevin spin glass dynamics." Ann. Probab. 25 (3) 1367 - 1422, July 1997.


Published: July 1997
First available in Project Euclid: 18 June 2002

zbMATH: 0954.60031
MathSciNet: MR1457623
Digital Object Identifier: 10.1214/aop/1024404517

Primary: 60F10 , 60H10 , 60K35 , 82C22 , 82C31 , 82C44

Keywords: Interacting random processes , Langevin dynamics , large deviations , statistical mechanics

Rights: Copyright © 1997 Institute of Mathematical Statistics


Vol.25 • No. 3 • July 1997
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