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Global geometry under isotropic Brownian flows

Vadlamani, Sreekar LU and Adler, Robert (2006) In Electronic Communications in Probability 11. p.182-192
Abstract
We consider global geometric properties of a codimension one manifold embedded in Euclideanspace, 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 globalperspective, rather than the local perspective, on which there is a much larger literature.
Please use this url to cite or link to this publication:
author
and
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Stochastic flows, Brownian flows, manifolds, Lipschitz-Killing curvatures, evolutionequations, Lyapunov exponents
in
Electronic Communications in Probability
volume
11
article number
19
pages
11 pages
publisher
Institute of Mathematical Statistics
external identifiers
  • scopus:33748566767
ISSN
1083-589X
DOI
10.1214/ECP.v11-1212
language
English
LU publication?
no
id
fae35d2c-963f-41e5-b5a2-d245c2f17c59
date added to LUP
2019-02-14 13:53:22
date last changed
2020-01-13 01:29:08
@article{fae35d2c-963f-41e5-b5a2-d245c2f17c59,
  abstract     = {We consider global geometric properties of a codimension one manifold embedded in Euclideanspace, 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 globalperspective, rather than the local perspective, on which there is a much larger literature.},
  author       = {Vadlamani, Sreekar and Adler, Robert},
  issn         = {1083-589X},
  language     = {eng},
  pages        = {182--192},
  publisher    = {Institute of Mathematical Statistics},
  series       = {Electronic Communications in Probability},
  title        = {Global geometry under isotropic Brownian flows},
  url          = {http://dx.doi.org/10.1214/ECP.v11-1212},
  doi          = {10.1214/ECP.v11-1212},
  volume       = {11},
  year         = {2006},
}