Georg Menz

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

We consider a noninteracting 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, Villani, Westdickenberg and the second author from the quadratic to the general case. Using an asymmetric Brascamp–Lieb-type inequality for covariances, we reduce the task of deriving a uniform LSI to the convexification of the coarse-grained Hamiltonian, which follows from a general local Cramer theorem.

Decay of Correlations in 1D Lattice Systems of Continuous Spins and Long-Range Interaction

We consider a one-dimensional lattice system of unbounded and continuous spins. The Hamiltonian consists of a perturbed strictly-convex single-site potential and a product term with longe-range interaction. We show that if the interactions have an algebraic decay of order

Poincaré and logarithmic Sobolev inequalities by decomposition of the energy landscape

2+\alpha

Hydrodynamic limit for conservative spin systems with super-quadratic, partially inhomogeneous single-site potential

2+α,

Approximate tensorization of entropy at high temperature

\alpha >0

A Brascamp-Lieb type covariance estimate

α>0, then the correlations also decay algebraically of order