| EPSRC Reference: |
GR/T26368/01 |
| Title: |
Random trees and forests in mathematical population models and cluster growth models driven by Levy processes |
| Principal Investigator: |
Winkel, Professor M |
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| Department: |
Statistics |
| Organisation: |
University of Oxford |
| Scheme: |
First Grant Scheme Pre-FEC |
| Starts: |
15 September 2004 |
Ends: |
14 January 2007 |
Value (£): |
114,724
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| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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Random trees and forests appear naturally in many biological and physical models. In population models, they describe the genealogy of a population evolving with time. In aggregating particle systems they arise either as collision history or as shapes in growth models. The aim of the research proposed here is to contribute to the literature on these models and particularly explore their connections.The central object of study is an extension of a growth model called the Stochastic Loewner Evolution (SLE), where we replace the driving Brownian motion by a more general Levy process. This leads to growing forests.Three areas of recent research will interplay1) SLE: The last five years have seen amazing progress relating lattice models in statistical physics to SLE via scaling limits.2) Real trees: Traditionally, random trees were studied through coding. Very recent work by Steve Evans (VR2) and co-authors, Berkeley, allows tostudy continuous random trees by a simple, transparent and direct method that gives new insight.3) Levy processes: There has been a hugely increased interest since the 1990s, in theory and applications. Relevant subareas include sample path properties, Levy-driven stochastic models and tree structures encoded by Levy 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 |
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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.ox.ac.uk |