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,
$|\!|\!| u |\!|\!| \;=\; \sum_{x\in \mathbb{Z}^d}
\Vert \partial_{\eta_x} u \Vert_\infty < \infty$.
Publié le : 2003-01-14
Classification:
Interacting particle systems,
polynomial convergence to equilibrium,
Nash inequality,
60K35,
82A05
@article{1046294306,
author = {Landim, C. and Yau, H. T.},
title = {Convergence to equilibrium of conservative particle systems on $\mathbb{Z}^{\bm{d}}$},
journal = {Ann. Probab.},
volume = {31},
number = {1},
year = {2003},
pages = { 115-147},
language = {en},
url = {http://dml.mathdoc.fr/item/1046294306}
}
Landim, C.; Yau, H. T. Convergence to equilibrium of conservative particle systems on $\mathbb{Z}^{\bm{d}}$. Ann. Probab., Tome 31 (2003) no. 1, pp. 115-147. http://gdmltest.u-ga.fr/item/1046294306/