Convergence to equilibrium of conservative particle systems on $\mathbb{Z}^{\bm{d}}$

Abstract

We consider the Ginzburg--Landau process on the lattice $\mathbb{Z}^d$ 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; that is, $|\!|\!| u |\!|\!| \;=\; \sum_{x\in \mathbb{Z}^d} \Vert \partial_{\eta_x} u \Vert_\infty < \infty$.