Appendices

Since{ˆri,a}ti= t+1 are absolutely continuous, we have for allk = i, P(ˆrji,a = ˆrjk,a) = 0and this yields Ωa = j PEa,j and Ea,j Ea,j = for allj = j . In particular, since|P| = t!we have pa = 1/(t!). Letϕa =(t 1) 1 The following result is used in the Proof of Lemma 5.2. Let 3 t T and recall that t = (t 1)/2 . To control the above integral, we provide a proper change of variables. Moreover, letR = (v1,...,vda) to be the corresponding change of basis matrix.