Construction of an Edwards ’ probability measure on C(R+, R)

In this article, we prove that the measures QT associated to the one-dimensional Edwards ’ model on the interval [0, T] converge to a limit measure Q when T goes to infinity, in the following sense: for all s ≥ 0 and for all events Λs depending on the canonical process only up to time s, QT (Λs) → Q(Λs). Moreover, we prove that, if P is Wiener measure, there exists a martin-gale (Ds)s∈R+ such that Q(Λs) = EP(1ΛsDs), and we give an explicit expression for this martingale. 1 Introduction and statement of the main theo-rems Edwards ’ model is a model for polymers chains, which is defined by considering Brownian motion "penalised " by the "quantity " of its self-intersections (see also [Edw65]). More precisely, for d ∈ N∗, and T> 0, let P(d)T be Wiener measur