| EPSRC Reference: |
GR/R81497/01 |
| Title: |
Random walks on graphs |
| Principal Investigator: |
Grigor'Yan, Professor A |
| Other Investigators: |
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| Department: |
Mathematics |
| Organisation: |
Imperial College London |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
11 November 2002 |
Ends: |
10 May 2005 |
Value (£): |
8,446
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| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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The classical random walk on the n-dimensional lattice admits Gaussian two-sided estimated for the heat kernel (=the transition probabilities). The recent development of analsyis on fractals has led to discovery of such graphs of fractals structure where the heat kernel behaves in a different way sub-Gaussian, featuring a slower propagation. An intriguing question is to understand the geometric reasons for such a phenomenon.Some results in this direction have been already obtained jointly by A.Grigor'yan and A.Telcs. They have shown the importance of such properties of the underlying space as volume doubling, certain estimates of mean exit time from a ball, elliptic Harnack inequality. The project is meant to be an extensive investigation of all aspects of sub-Gaussian heat kernel behaviour.
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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 |
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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 |