| EPSRC Reference: |
EP/G056390/1 |
| Title: |
On models of random permutations with cycle weights and spatial structure |
| Principal Investigator: |
Ueltschi, Dr D |
| Other Investigators: |
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| Researcher Co-Investigators: |
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| Project Partners: |
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| Department: |
Mathematics |
| Organisation: |
University of Warwick |
| Scheme: |
First Grant Scheme |
| Starts: |
31 March 2010 |
Ends: |
30 March 2014 |
Value (£): |
247,716
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| EPSRC Research Topic Classifications: |
| Mathematical Physics |
Statistics & Appl. Probability |
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| EPSRC Industrial Sector Classifications: |
| No relevance to Underpinning Sectors |
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| Related Grants: |
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| Panel History: |
| Panel Date | Panel Name | Outcome |
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05 Mar 2009
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Mathematics Prioritisation Panel
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Announced
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Summary on Grant Application Form |
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Random permutations have been a hot topic in probability theory and applied mathematics because of their connections to random matrices and other systems. The present study goes beyond the uniform permutations that have been considered so far. Of interest for us will be models where permutations receive a weight that depends on their cycle distribution. Another model of interest involves permutations of points in the space, with a weight that depends on the length of the permutation jumps. The main question deals with the possible occurrence of infinite cycles.These models find their origin in two unrelated areas. First, they describe the phenomenon of Bose-Einstein condensation, which is a phase transition that occurs for large systems of bosonic quantum particles. Second, they describe alleles in haploid populations, which are very much studied in mathematical biology.Results are expected to have consequences beyond mathematics. In particular, they will help the physicists to understand the effects of the particle interactions on the Bose-Einstein condensation. Indeed, models of spatial permutations are simpler, yet they describe quantum systems exactly. Thus they will allow for more detailed results.
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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.warwick.ac.uk |