Disertori, Margherita; Merkl, Franz; Rolles, Silke W. W.
(2016):
A comparison of a nonlinear sigma model with general pinning and pinning at one point.
In: Electronic Journal of Probability, Vol. 21, 27

Full text not available from 'Open Access LMU'.
Abstract
We study the nonlinear supersymmetric hyperbolic sigma model introduced by Zirnbauer in 1991. This model can be related to the mixing measure of a vertexreinforced jump process. We prove that the twopoint correlation function has a probabilistic interpretation in terms of connectivity in rooted random spanning forests. Using this interpretation, we dominate the twopoint correlation function for general pinning, e.g. for uniform pinning, with the corresponding correlation function with pinning at one point. The result holds for a general finite graph, asymptotically as the strength of the pinning converges to zero. Specializing this to general ladder graphs, we deduce in the same asymptotic regime exponential decay of correlations for general pinning.