Sanov results for Glauber spin-glass dynamics
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- Grunwald, M. Probab Theory Relat Fields (1996) 106: 187. doi:10.1007/s004400050062
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In this paper we prove a Sanov result, i.e. a Large Deviation Principle (LDP) for the distribution of the empirical measure, for the annealed Glauber dynamics of the Sherrington-Kirkpatrick spin-glass. Without restrictions on time or temperature we prove a full LDP for the asymmetric dynamics and the crucial upper large deviations bound for the symmetric dynamics. In the symmetric model a new order-parameter arises corresponding to the response function in [SoZi83]. In the asymmetric case we show that the corresponding rate function has a unique minimum, given as the solution of a self-consistent equation. The key argument used in the proofs is a general result for mixing of what is known as Large Deviation Systems (LDS) with measures obeying an independent LDP.