| EPSRC Reference: |
GR/M61573/01 |
| Title: |
DIFFUSION PROCESSES ON RIEMANNIAN MANIFOLDS |
| Principal Investigator: |
Grigor'Yan, Professor A |
| Other Investigators: |
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| Department: |
Mathematics |
| Organisation: |
Imperial College London |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
23 March 1999 |
Ends: |
22 June 2001 |
Value (£): |
6,000
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| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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The main aim of the project is to develop new methods of investigating of trajectories of Brownian motion on Riemannian manifolds. The existing methods in Euclidean spaces are frequently linked to specific properties of such spaces like translation invariance etc. One of the questions to be considered is the escape rate of the Brownian motion on manifolds of superpolynomial volume growth (our previous work solved the question for the polynomial growth). Another direction is the asymptotic proximity property of several independent Brownian trajectories. Our preliminary results give us an insight into this question providing the link with the heat kernel long time decay. Further investigations are required to achieve the full answer. The third important direction is the study of the branching processes on manifolds. Practically nothing is known so far, and we plan to start with the very basic questions such as geometric conditions for recurrence and transience for such processes.
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Key Findings |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Potential use in non-academic contexts |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Impacts |
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| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
| Summary |
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| Date Materialised |
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Sectors submitted by the Researcher |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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| Project URL: |
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| Further Information: |
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| Organisation Website: |
http://www.imperial.ac.uk |