Preprint A73/2001
Convergence to equilibrium of conservative particle systems on $\bb Z^d$

Horng-Tzer Yau | Landim, Claudio

**Keywords: **
markov processes | polynomial convergence to equilibrium | conservative dynamics

We consider the Ginzburg-Landau process on the lattice $\bb Z^d$
whose potential is a bounded perturbation of the Gaussian potential.
We prove that the decay rate to equilibrium in the variance sense is
$t^{-d/2}$ up to a logarithmic correction, for any function $u$ with
finite triple norm, i.e., $|\!|\!| u |\!|\!| \;=\; \sum_{x\in \bb
Z^d} \Vert \partial_{\eta_x} u \Vert_\infty < \infty$.