Space-time Correlations of a Gaussian Interface
2010, v.16, Issue 1, 205-222
The serial harness introduced by Hammersley [J.M. Hammersley, Harnesses. In: Proc. Fifth Berkeley Sympos. Mathematical Statistics and Probability, 1966, Vol. III, 89-117] is equivalent, in the Gaussian case, to the Gaussian Solid-On-Solid interface model with parallel heat bath dynamics. Here we consider sub-lattice parallel dynamics, and give exact results about relaxation dynamics, based on the equivalence to the infinite time limit of a time periodic random field. We also give a numerical comparison to the harness process in continuous time studied by Hsiao [C.-T. Hsiao, Stochastic processes with Gaussian interaction of components. Z. Wahrsch. Verw. Geb., 1982, v. 59, 39-53] and by Ferrari, Niederhauser and Pechersky [P.A. Ferrari and B.M. Niederhauser, Harness processes and harmonic crystals. Stoch. Process. Appl., 2006, v. 116, 939-956, math.PR/0312402; P.A. Ferrari, B.M. Niederhauser and E.A. Pechersky, Harness processes and non-homogeneous crystals. J. Stat. Phys., 2007, v. 128, 1159-1176, math.PR/0409301].
Keywords: random surface,interface dynamics,harness