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

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., $|\!|\!| u |\!|\!| \;=\; \sum_{x\in \bb Z^d} \Vert \partial_{\eta_x} u \Vert_\infty < \infty$.