2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/104695In this note we study a class of specifications over $d$-dimensional Wiener measure which are invariant under uniform translation of the paths. This degeneracy is removed by restricting the measure to the $σ$-algebra generated by the increments of the coordinate process. We address the problem of existence and uniqueness of Gibbs measures and prove a central limit theorem for the rescaled increments. These results apply to the study of the ground state of the Nelson model of a quantum particle interacting with a scalar boson field.15 pages, no figures; typos, details added to the proofsMathematical Physics82B21text