

Preprint 31/2010
LSI for Kawasaki dynamics with weak interaction
Georg Menz
Contact the author: Please use for correspondence this email.
Submission date: 07. Jun. 2010
Pages: 61
published in: Communications in mathematical physics, 307 (2011) 3, p. 817-860
DOI number (of the published article): 10.1007/s00220-011-1326-6
Bibtex
MSC-Numbers: 60K35, 60J25, 82B21
Keywords and phrases: Logarithmic Sobolev inequality, Spin system, Kawasaki dynamics, Canonical ensemble, coarse-graining
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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.