A new criterion for the logarithmic Sobolev inequality and two applications
نویسندگان
چکیده
We present 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.
منابع مشابه
Logarithmic Sobolev inequality for diffusion semigroups
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