Statistical properties of the 2D attached Rouse chain

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We study various dynamical properties (winding angles, areas) of a set of harmonically bound Brownian particles (monomers), one endpoint of this chain being kept fixed at the origin 0. In particular, we show that, for long times t, the areas Aᵢ enclosed by the monomers scale like t¹/², with correlated gaussian distributions. This is at variance with the winding angles θᵢ around fixed points that scale like t and are distributed according to independent Cauchy laws.