Gibbs Measures for Self-Interacting Wiener Paths

M. Gubinelli

2006, v.12, №4, 747-766

ABSTRACT

We study a class of specifications over $d$-dimensional Wiener measure which are invariant under translation of the paths. We address the problem of existence and uniqueness of the Gibbs measures and prove a central limit theorem for the rescaled process. These results apply to the study of the ground state of the Nelson model of a quantum particle interacting with a scalar boson field.

Keywords: Gibbs measures,Nelson model,scaling limits

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