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 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∞.
Original language | English (US) |
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Pages (from-to) | 211-255 |
Number of pages | 45 |
Journal | Stochastic Processes and their Applications |
Volume | 105 |
Issue number | 2 |
DOIs | |
State | Published - Jun 1 2003 |
Keywords
- Disordered systems
- Interacting diffusion processes
- Large deviations
- Statistical mechanics
ASJC Scopus subject areas
- Statistics and Probability
- Modeling and Simulation
- Applied Mathematics