Georg Menz (MPI Leipzig)
Title: Log-Sobolev inequality for Kawasaki dynamics with superquadratic single-site potential.
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
SLIDES deterministic_ginzburg.mov ginzburg.mov