Potential Analysis

, Volume 34, Issue 1, pp 23–41

A Brownian Motion on the Diffeomorphism Group of the Circle


DOI: 10.1007/s11118-010-9178-9

Cite this article as:
Wu, M. Potential Anal (2011) 34: 23. doi:10.1007/s11118-010-9178-9


Let Diff(S1) be the group of orientation preserving C ∞  diffeomorphisms of S1. In 1999, P. Malliavin and then in 2002, S. Fang constructed a canonical Brownian motion associated with the H3/2 metric on the Lie algebra diff(S1). The canonical Brownian motion they constructed lives in the group Homeo(S1) of Hölderian homeomorphisms of S1, which is larger than the group Diff(S1). In this paper, we present another way to construct a Brownian motion that lives in the group Diff(S1), rather than in the larger group Homeo(S1).


Diffeomorphism groupBrownian motionStochastic differential equation

Mathematics Subject Classifications (2010)


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© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of ConnecticutStorrsUSA