The Annals of Probability

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

C. Landim and H. T. Yau

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

Article information

Source
Ann. Probab., Volume 31, Number 1 (2003), 115-147.

Dates
First available in Project Euclid: 26 February 2003

Permanent link to this document
https://projecteuclid.org/euclid.aop/1046294306

Digital Object Identifier
doi:10.1214/aop/1046294306

Mathematical Reviews number (MathSciNet)
MR1959788

Zentralblatt MATH identifier
1015.60098

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 82A05

Keywords
Interacting particle systems polynomial convergence to equilibrium Nash inequality

Citation

Landim, C.; Yau, H. T. Convergence to equilibrium of conservative particle systems on $\mathbb{Z}^{\bm{d}}$. Ann. Probab. 31 (2003), no. 1, 115--147. doi:10.1214/aop/1046294306. https://projecteuclid.org/euclid.aop/1046294306


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  • NEW YORK, NEW YORK 10003 E-MAIL: yau@cims.ny u.edu