Georg Menz (MPI Leipzig)

Title:  Log-Sobolev inequality for Kawasaki dynamics with superquadratic single-site potential.


In this talk about a joint work with Felix Otto, we consider a non-interacting unbounded spin system with conservation of the mean spin. We derive a uniform log-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, Westdickenberg, and Villani 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 Cramèr theorem.