Uniform logarithmic Sobolev inequalities for conservative spin systems with super-quadratic single-site potential

Uniform logarithmic Sobolev inequalities for conservative spin systems with super-quadratic single-site potential

We consider a non-interacting unbounded spin system with conservation of the mean spin. We derive a uniform logarithmic Sobolev inequality (LSI) provided the single-site potential is a bounded perturbation of a strictly convex function. The scaling of the LSI constant is optimal in the system size. The argument adapts the two-scale approach of Grunewald, Otto, West-dickenberg, and Villani from ...

A Remark on Spectral Gap and Logarithmic Sobolev Inequalities for Conservative Spin Systems

We observe that a class of conditional probability measures for unbounded spin systems with convex interactions satisses Poincar e and logarithmic Sobolev inequalities. For the corresponding conservative dynamics in a box of linear size L we show that the inverse of the spectral gap and the logarithmic Sobolev constant scale as L 2 in any dimension. 2000 MSC: 60K35

Logarithmic Sobolev Inequalities for Unbounded Spin Systems Revisited

where Entμ(f ) is the entropy of f with respect to μ (see below). It is well-known that the product measure μ of μ on R then satisfies the preceding inequalities (with the Euclidean length of the gradient of the function f on R) with the same constant C, in particular independent of the dimension n. Let now H be a smooth function on R such that ∫ edμ < ∞. Define Q the probability measure on R w...

Perturbing the Logarithmic Sobolev Inequality for Unbounded Spin Systems on the Lattice with Non Quadratic Interactions

Abstract. We consider unbounded spin systems on the one dimensional Lattice with interactions that go beyond the usual strict convexity and without uniform bound on the second derivative. We assume that the one dimensional without interactions (boundary-free) measure satisfies the Log-sobolev inequality and we determine conditions under which the Log-Sobolev Inequality can be extended to the in...

Modified logarithmic Sobolev inequalities and transportation inequalities