 Large deviations in the Langevin dynamics of a random field Ising modelGérard Ben Arous and Michel Sortais Stochastic Processes and their Applications, 2003, vol. 105, issue 2, 211-255 Abstract: 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 having a unique minimiser Q[infinity]. The asymptotic dynamics Q[infinity] 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 [Psi] 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 satisfying: , 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[infinity]. Keywords: Large; deviations; Statistical; mechanics; Disordered; systems; Interacting; diffusion; processes (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:105:y:2003:i:2:p:211-255 Ordering information: This journal article can be ordered from Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
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