Windings of the 2D free Rouse chain

We study the long-time dynamical properties of a chain of harmonically boun d Brownian particles. This chain is allowed to wander everywhere in the pla ne. We show that the scaling variables for the occupation times T-j, areas A(j) and winding angles theta (j) (j = 1 , . . . , n labels the particles) take the same general form as in the usual Brownian motion. We also compute the asymptotic joint laws P({T-j}), P({A(j)}), P({theta (j)}) and discuss the correlations occurring in those distributions.