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LSI for Kawasaki Dynamics with Weak Interaction

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Abstract

We consider a large lattice system of unbounded continuous spins that are governed by a Ginzburg-Landau type potential and a weak quadratic interaction. We derive the logarithmic Sobolev inequality (LSI) for Kawasaki dynamics uniform in the boundary data. The scaling of the LSI constant is optimal in the system size and our argument is independent of the geometric structure of the system. The proof consists of an application of the two-scale approach of Grunewald, Otto, Westdickenberg & Villani. Several ideas are needed to solve new technical difficulties due to the interaction. Let us mention the application of a new covariance estimate, a conditioning technique, and a generalization of the local Cramér theorem.

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  1. Max Planck Institute for Mathematics in the Sciences, Inselstr. 22 - 26, Leipzig, Germany

    Georg Menz

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  1. Georg Menz
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Correspondence to Georg Menz.

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Communicated by H.-T. Yau

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Menz, G. LSI for Kawasaki Dynamics with Weak Interaction. Commun. Math. Phys. 307, 817–860 (2011). https://doi.org/10.1007/s00220-011-1326-6

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  • DOI: https://doi.org/10.1007/s00220-011-1326-6

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