Interface Fluctuations in a Conserved System: Derivation and Long Time Behaviour,
2003, v.9, Issue 1, 1-34
We study a simple model for interface fluctuations which can be seen as a simplified version of the stochastic phase field equations in one space dimension. In a suitable scaling limit, the front evolves according to a linear stochastic ODE with a long memory drift. We then study the long time behaviour of the limiting process proving an invariance principle; the latter can also be obtained directly from the original process. We note the model can be interpreted as a Brownian motion weakly coupled to a random environment whose evolution depends on the location of the Brownian motion. The limiting process is non-Markovian and exhibits aging effects.
Keywords: stochastic equations,interface dynamics,invarianceprinciple,random walk in random environment