A Brownian Motion on the Group of Diffeomorphisms of the Circle

2009/09/22 by Wu, Mang
#FOS: Mathematics #Functional Analysis (math.FA) #Probability (math.PR)

paper · doi:10.48550/arxiv.0909.3881

Abstract

The canonical Brownian motion that P. Malliavin in 1999 and then S. Fang in 2002 constructed lives in the group of Holderian homeomorphisms of the circle. In this paper, we present another way to construct a Brownian motion that lives exactly in the group of orientation preserving smooth diffeomorphisms of the circle.

Related

• Diffeomorphisms of the circle and Brownian motions on an infinite-dimensional symplectic group
• Groups of Circle Diffeomorphisms
• Brownian motion and Ricci curvature on an infinite dimensional symplectic group related to the diffeomorphism group of the circle
• Dyson Brownian Motion and motion by mean curvature
• Brownian path preserving mappings on the Heisenberg group