Equivalence of decay of correlations, the log-Sobolev inequality, and of the spectral gap

Wednesday, November 19, 2014 -
2:00pm to 3:00pm
In this talk we consider a lattice system of unbounded real-valued spins, which is described by its Gibbs measure mu. We discuss how a known result for finite-range interaction is generalized to infinite-range. The result states that it is equivalent: The correlations of the Gibbs measure mu decay, the Gibbs measure mu satisfies a log-Sobolev inequality uniformly in the systems size and the boundary values, and mu satisfies a uniform spectral gap. Such a statement is interesting, because it connects a static property of the equilibrium state mu of the system to a dynamic property of the system i.e. how fast the Glauber dynamics converges to equilibrium.
Georg Menz
Stanford University
Event Location: 
Fine Hall 322