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global geometry under isotropic brownian Sreekar Vadlamani
 

Summary: global geometry under isotropic brownian
flows
Sreekar Vadlamani
and Robert J. Adler
February 7, 2006
Abstract
We consider global geometric properties of a codimension one manifold embedded
in Euclidean space, as it evolves under an isotropic and volume preserving Brownian
flow of diffeomorphisms. In particular, we obtain expressions describing the expected
rate of growth of the Lipschitz-Killing curvatures, or intrinsic volumes, of the manifold
under the flow.
These results shed new light on some of the intriguing growth properties of flows
from a global perspective, rather than the local perspective, on which there is a much
larger literature.
1 Introduction
We are interested in Brownian flows st, 0 s t < from Rn Rn, obtained by
solving the collection of stochastic differential equations
xt = t(x) = x +
t
0

  

Source: Adler, Robert J. - Faculty of Industrial Engineering and Management, Technion, Israel Institute of Technology

 

Collections: Mathematics; Engineering