Global geometry under isotropic Brownian flows
(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:
https://lup.lub.lu.se/record/fae35d2c-963f-41e5-b5a2-d245c2f17c59
- author
- Vadlamani, Sreekar LU and Adler, Robert
- publishing date
- 2006
- 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
- 2022-01-31 17:43:06
@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}},
keywords = {{Stochastic flows; Brownian flows; manifolds; Lipschitz-Killing curvatures; evolutionequations; Lyapunov exponents}},
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}},
}