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SEMINARI DI CALCOLO DELLE PROBABILITA`
Mercoledi' 29 Febbraio 2012, alle 15:00 in aula 2AB40 della Torre Archimede, il Prof. Georg Menz (Max-Planck-Institut für Mathematik) terra' un seminario dal titolo "Log-Sobolev inequality for Kawasaki dynamics".
We consider a non-interacting unbounded spin system with conservation of the mean spin. In the first part of the talk, we will derive a uniform log-Sobolev inequality (LSI) for a weakly-interacting Hamiltonian. 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 non-interacting to the interacting case. Due to technical reasons, this approach is limited to single-site potentials that are bounded perturbations of a quadratic potential. In the second part of the talk, we will show that --at least in the non-interacting case-- one can weaken this assumption to single-site potentials that are bounded perturbations of strictly convex functions. For this reason one has to apply an iterative argument. The core of the iteration is an asymmetric Brascamp-Lieb type inequality for covariances. The second part of the talk is about a joint work with Felix Otto.
Rif. int. P. Dai Pra