| EPSRC Reference: |
EP/C515056/1 |
| Title: |
Random Matrices and Polynomials: a tool to understand complexity |
| Principal Investigator: |
Fyodorov, Professor Y |
| Other Investigators: |
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| Project Partners: |
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| Department: |
Sch of Mathematical Sciences |
| Organisation: |
University of Nottingham |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
26 September 2005 |
Ends: |
25 September 2008 |
Value (£): |
163,124
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| EPSRC Research Topic Classifications: |
| Mathematical Analysis |
Non-linear Systems Mathematics |
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| EPSRC Industrial Sector Classifications: |
| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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Complexity is an interdisciplinary concept which, in particular, addressesthe question of how order emerges out of randomness and interactions. For many reasons random matrices provide a very practical and powerful tool in approaching and quantifying the related characteristics.We are going to use recently advanced random matrix techniques and ideas to provide, in particular (i) Explicit and mathematically controllable statistical characterisation of landscape complexity (i.e. the number of minima, maxima, and saddle-points of various types)for random energy landscapes in disordered systemswith glassy dynamics (manifolds in random environment, systems with random fields, etc. ). (ii) ways of establishing probabilistic criteria of stability, as well as dynamic propertiesof complex linear systems with inherent structural uncertainty.(iii) investigation of statistics of roots for various types of random polynomials (polynomials with random coefficients, as well as so called permanental polynomials generated by random matrices), with emphasis on universality of the obtained results (i.e. insensitivity to thedetails of particular models considered).
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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.nottingham.ac.uk |