Baxendale, Peter; Harris, Theodore E. Isotropic stochastic flows. (English) Zbl 0606.60014 Ann. Probab. 14, 1155-1179 (1986). Various results on homogeneous isotropic stochastic flows in Euclidean space \({\mathbb{R}}^ d\) are gathered here. Being mainly formulated in terms of a decomposition of the flow into a potential (curl-free) and a solenoidal (divergence-free) part they include characterizations of the asymptotic behaviour of two point distances (which turns out to be different for \(d=2\), \(d=3\) or \(d\geq 4\), respectively) and of angle-length relations between pairs of tangent vectors - e.g., tangent vectors line up asymptotically, which is proved without explicitly using the fact that the two leading Lyapunov exponents are distinct. Further an analogue of the curl-free property is derived for potential isotropic flows and estimates of the lengths of arcs under the flow are given in dependence of their shapes. The paper concludes with a brief discussion of homogeneous nonisotropic flows. Reviewer: H.Crauel Cited in 39 Documents MSC: 60B99 Probability theory on algebraic and topological structures 60G99 Stochastic processes Keywords:homogeneous isotropic stochastic flows; Lyapunov exponents; potential isotropic flows; homogeneous nonisotropic flows × Cite Format Result Cite Review PDF Full Text: DOI