Skip to content Skip to navigation
University of Warwick
  • Study
  • |
  • Research
  • |
  • Business
  • |
  • Alumni
  • |
  • News
  • |
  • About

University of Warwick
Publications service & WRAP

Highlight your research

  • WRAP
    • Home
    • Search WRAP
    • Browse by Warwick Author
    • Browse WRAP by Year
    • Browse WRAP by Subject
    • Browse WRAP by Department
    • Browse WRAP by Funder
    • Browse Theses by Department
  • Publications Service
    • Home
    • Search Publications Service
    • Browse by Warwick Author
    • Browse Publications service by Year
    • Browse Publications service by Subject
    • Browse Publications service by Department
    • Browse Publications service by Funder
  • Help & Advice
University of Warwick

The Library

  • Login
  • Admin

Homogenisation on homogeneous spaces

Tools
- Tools
+ Tools

Li, X-M. (2018) Homogenisation on homogeneous spaces. Journal of the Mathematical Society of Japan, 70 (2). pp. 519-572. doi:10.2969/jmsj/07027546 ISSN 0025-5645.

[img]
Preview
PDF
WRAP-homogenisation-spaces-Li-2017.pdf - Accepted Version - Requires a PDF viewer.

Download (1100Kb) | Preview
Official URL: http://doi.org/10.2969/jmsj/07027546

Request Changes to record.

Abstract

Motivated by collapsing of Riemannian manifolds and inhomogeneous scaling of left invariant Riemannian metrics on a real Lie group G with a sub-group H, we consider a family of stochastic differential equations (SDEs) on G with parameter ϵ>0 and Markov generator Lϵ=1ϵ∑k(Ak)2+1ϵA0+Y0 where Y0,Ak are left invariant vector fields and {Ak} generate the Lie-algebra of H. Assuming that G/H is a reductive homogeneous space, in the sense of Nomizu, we study the solutions of the SDE as ϵ approaches zero.
We use the projection as a `conservation law' and obtain a family of slow variables: these are random variables, parameterized by ϵ, evolving in time. We examine their convergence on the time interval [0,1] and on [0,1ϵ], and study their effective motions. The effective motions on G over the larger time scale are Markov processes, which can be classified algebraically by a real Peter Weyl theorem and geometrically using a weak notion of the naturally reductive property; the classifications allow us to conclude when their projections to the homogeneous space G/H are Markov.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH): Homogenization (Differential equations), Homogeneous spaces
Journal or Publication Title: Journal of the Mathematical Society of Japan
Publisher: Maths Society Japan
ISSN: 0025-5645
Official Date: 18 April 2018
Dates:
DateEvent
18 April 2018Published
30 July 2017Available
6 February 2017Accepted
Volume: 70
Number: 2
Page Range: pp. 519-572
DOI: 10.2969/jmsj/07027546
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access
Date of first compliant deposit: 8 March 2017
Date of first compliant Open Access: 1 May 2019
Related URLs:
  • Publisher

Request changes or add full text files to a record

Repository staff actions (login required)

View Item View Item

Downloads

Downloads per month over past year

View more statistics

twitter

Email us: wrap@warwick.ac.uk
Contact Details
About Us