, Volume 156, Issue 2, pp 399-433

Spectral gap and logarithmic Sobolev inequality for Kawasaki and Glauber dynamics

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Abstract

We prove that the spectral gap of the Kawasaki dynamics shrink at the rate of 1/L 2 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.

Research partially supported by U.S. National Science Foundation grant 9101196, Sloan Foundation Fellowship and David and Lucile Packard Foundation Fellowship
Communicated by J.L. Lebowitz