## Abstract

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.

Original language | English (US) |
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Pages (from-to) | 1367-1422 |

Number of pages | 56 |

Journal | Annals of Probability |

Volume | 25 |

Issue number | 3 |

DOIs | |

State | Published - Jul 1997 |

## Keywords

- Interacting random processes
- Langevin dynamics
- Large deviations
- Statistical mechanics

## ASJC Scopus subject areas

- Statistics and Probability
- Statistics, Probability and Uncertainty