TY - JOUR
T1 - Large deviations in the Langevin dynamics of a random field Ising model
AU - Arous, Gérard Ben
AU - Sortais, Michel
N1 - Funding Information:
The second author gratefully acknowledges financial support from the Swiss National Science Foundation.
PY - 2003/6/1
Y1 - 2003/6/1
N2 - 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∞.
AB - 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∞.
KW - Disordered systems
KW - Interacting diffusion processes
KW - Large deviations
KW - Statistical mechanics
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U2 - 10.1016/S0304-4149(02)00265-X
DO - 10.1016/S0304-4149(02)00265-X
M3 - Article
AN - SCOPUS:0038406213
SN - 0304-4149
VL - 105
SP - 211
EP - 255
JO - Stochastic Processes and their Applications
JF - Stochastic Processes and their Applications
IS - 2
ER -