2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/68353We study a Gibbs measure over Brownian motion with a pair potential which depends only on the increments. Assuming a particular form of this pair potential, we establish that in the infinite volume limit the Gibbs measure can be viewed as Brownian motion moving in a dynamic random environment. Thereby we are in a position to use the technique of Kipnis and Varadhan and to prove a functional central limit theorem.19 pagesProbabilityMathematical Physics60F17text