A semicircle law and decorrelation for iterated Kolmogorov loops (Karen Habermann, Hausdorff Center for Mathematics, Bonn)

29.04.2019 15:15 – 16:15

We consider a standard one-dimensional Brownian motion on [0,1] conditioned to have vanishing iterated time integrals up to order N. We show that the resulting processes converge weakly to the zero process as N tends to infinity. We further study the fluctuation processes and show that they converge in finite dimensional distributions to a collection of independent zero-mean Gaussian random variables whose variances follow a scaled semicircle.

Lieu

Room 17, Séminaire "Mathématique Physique"

entrée libre