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Communications in Mathematical Physics

, Volume 156, Issue 2, pp 399–433 | Cite as

Spectral gap and logarithmic Sobolev inequality for Kawasaki and Glauber dynamics

  • Sheng Lin Lu
  • Horng-Tzer Yau
Article

Abstract

We prove that the spectral gap of the Kawasaki dynamics shrink at the rate of 1/L2 for cubes of sizeL provided that some mixing conditions are satisfied. We also prove that the logarithmic Sobolev inequality for the Glauber dynamics in standard cubes holds uniformly in the size of the cube if the Dobrushin-Shlosman mixing condition holds for standard cubes.

Keywords

Neural Network Statistical Physic Complex System Nonlinear Dynamics Quantum Computing 
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Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • Sheng Lin Lu
    • 1
  • Horng-Tzer Yau
    • 2
  1. 1.Department of MathematicsUniversity of MichiganAnn ArborUSA
  2. 2.Courant InstituteNew York UniversityNew YorkUSA

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