Equivalence of decay of correlations, the logSobolev inequality, and of the spectral gap
Equivalence of decay of correlations, the logSobolev inequality, and of the spectral gap

Georg Menz, Stanford University
Fine Hall 322
In this talk we consider a lattice system of unbounded realvalued spins, which is described by its Gibbs measure mu. We discuss how a known result for finiterange interaction is generalized to infiniterange. The result states that it is equivalent: The correlations of the Gibbs measure mu decay, the Gibbs measure mu satisfies a logSobolev 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.