Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4592825 | Journal of Functional Analysis | 2007 | 37 Pages |
Abstract
We give a criterion for the logarithmic Sobolev inequality (LSI) on the product space X1×⋯×XN. We have in mind an N-site lattice, unbounded continuous spin variables, and Glauber dynamics. The interactions are described by the Hamiltonian H of the Gibbs measure. The criterion for LSI is formulated in terms of the LSI constants of the single-site conditional measures and the size of the off-diagonal entries of the Hessian of H. It is optimal for Gaussians with positive covariance matrix. To illustrate, we give two applications: one with weak interactions and one with strong interactions and a decay of correlations condition.
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