Large deviations in the Langevin dynamics of a random field Ising model
Autor: | Gérard Ben Arous, Michel Sortais |
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Rok vydání: | 2003 |
Předmět: |
Statistics and Probability
Random field Applied Mathematics Random walk Interacting diffusion processes Langevin equation symbols.namesake Disordered systems Large deviations Modeling and Simulation Modelling and Simulation symbols Large deviations theory Ising model Gibbs measure Langevin dynamics Rate function Statistical mechanics Mathematics Mathematical physics |
Zdroj: | Stochastic Processes and their Applications. 105(2):211-255 |
ISSN: | 0304-4149 |
DOI: | 10.1016/s0304-4149(02)00265-x |
Popis: | We consider a Langevin dynamics scheme for a d-dimensional Ising model with a disordered external magnetic field and establish that the averaged law of the empirical process obeys a large deviation principle (LDP), according to a good rate functional Ja having a unique minimiser Q∞. The asymptotic dynamics Q∞ may be viewed as the unique weak solution associated with an infinite-dimensional system of interacting diffusions, as well as the unique Gibbs measure corresponding to an interaction Ψ on infinite dimensional path space. We then show that the quenched law of the empirical process also obeys a LDP, according to a deterministic good rate functional Jq satisfying: Jq⩾Ja, so that (for a typical realisation of the disordered external magnetic field) the quenched law of the empirical process converges exponentially fast to a Dirac mass concentrated at Q∞. |
Databáze: | OpenAIRE |
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