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January 2003 Convergence to equilibrium of conservative particle systems on $\mathbb{Z}^{\bm{d}}$
C. Landim, H. T. Yau
Ann. Probab. 31(1): 115-147 (January 2003). DOI: 10.1214/aop/1046294306

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

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C. Landim. H. T. Yau. "Convergence to equilibrium of conservative particle systems on $\mathbb{Z}^{\bm{d}}$." Ann. Probab. 31 (1) 115 - 147, January 2003. https://doi.org/10.1214/aop/1046294306

Information

Published: January 2003
First available in Project Euclid: 26 February 2003

zbMATH: 1015.60098
MathSciNet: MR1959788
Digital Object Identifier: 10.1214/aop/1046294306

Subjects:
Primary: 60K35 , 82A05

Keywords: interacting particle systems , Nash inequality , polynomial convergence to equilibrium

Rights: Copyright © 2003 Institute of Mathematical Statistics

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Vol.31 • No. 1 • January 2003
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