Motion by mean curvature from the Ginzburg-Landau \(\nabla\phi\) interface model (Q1357442)

For a certain scalar field \(\varphi_t\) with reversible stochastic dynamics the authors show that under a suitable large scale limit the field becomes deterministic such that locally its normal velocity is proportional to its mean curvature (except to some anisotropy effect). Unlike many other works showing the deterministic behaviour of a stochastic system, here no conservation law is assumed. As a result, it is shown that for every tilt the above field has a unique shift-invariant, ergodic Gibbs measure for \(\nabla \varphi\)-field.