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The log-Sobolev inequality for weakly coupled lattice fields
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  • Published: August 1999

The log-Sobolev inequality for weakly coupled lattice fields

  • Nobuo Yoshida1 

Probability Theory and Related Fields volume 115, pages 1–40 (1999)Cite this article

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Abstract.

We consider a ferromagnetic spin system with unbounded interactions on the d-dimensional integer lattice (d > 1). Under mild assumptions on the one-body interactions (so that arbitrarily deep double wells are allowed), we prove that if the coupling constants are small enough, then the finite volume Gibbs states satisfy the log-Sobolev inequality uniformly in the volume and the boundary condition.

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Authors and Affiliations

  1. Division of Mathematics, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan. e-mail: nobuo@kusm.kyoto-u.ac.jp, , , , , , JP

    Nobuo Yoshida

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  1. Nobuo Yoshida
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Received: 11 November 1997 / Revised version: 17 July 1998

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Yoshida, N. The log-Sobolev inequality for weakly coupled lattice fields. Probab Theory Relat Fields 115, 1–40 (1999). https://doi.org/10.1007/s004400050235

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  • Issue Date: August 1999

  • DOI: https://doi.org/10.1007/s004400050235

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  • Key wordsMathematics Subject Classification (1991): 60K35, 82B20
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