Abstract
We study isotropic Brownian flows on homogeneous spaces and particularly on the sphere S d−1 . An isotropic Brownian flow is directed by ξ an isotropic Gaussian vector field and therefore is characterized by a covariance matrix. Using the irreducible representations of SO(d), we calculate this covariance matrix. Given this covariance matrix, we compute the Lyapounov exponents of the flow, which describe its asymptotic behavior. In particular, we see that for d ≤ 5 a gradient flow is always stable.
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