Modulus of continuity of the canonic Brownian motion ``on the group of diffeomorphisms of the circle''
The Brownian motion \((g_t)\) on the group of \(C^\infty\)-diffeomorphisms on \(\mathbb{S}^1\), equipped with the so-called \(H^{3/2}\) metric, presents a decrease of regularity as time \(t\) goes by. The aim of this work is to supply a lower bound for the remaining Hölder regularity at time \(t>0\). So the main result asserts that the law of \(g_t\) is carried by \(\alpha\)-Hölder diffeomorphisms, for all \(\alpha<(1-\sqrt{1-e^{-t/2}}) /(1+\sqrt{1-e^{-t/2}})\). The method uses a study of the two-points process \((g_t(\theta), g_t(\theta'))\), showing in particular that no confluence takes place.
scientific article; zbMATH DE number 1888375
scientific article