EPSRC Reference: |
EP/V048902/1 |
Title: |
Noncommutative statistical mechanics: probability at the confluence |
Principal Investigator: |
Blitvic, Dr N |
Other Investigators: |
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Researcher Co-Investigators: |
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Project Partners: |
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Department: |
Mathematics and Statistics |
Organisation: |
Lancaster University |
Scheme: |
Standard Research - NR1 |
Starts: |
31 July 2021 |
Ends: |
31 August 2022 |
Value (£): |
201,866
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EPSRC Research Topic Classifications: |
Logic & Combinatorics |
Mathematical Analysis |
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: |
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Summary on Grant Application Form |
The asymmetric simple exclusion process (ASEP) is a fundamental mathematical construction in statistical mechanics that combines the notion of stochastic motion with a physical requirement that matter cannot coexist in the same location. As such, it has wide-ranging applications, from traffic and fluid flow to biological processes. However, recent advances, particularly the emerging parallelism between ASEP-type processes and well-known families of orthogonal polynomials, hint at a hidden probabilistic phenomenon that promises to greatly expand the applicability of the ASEP.
The key is in a common computational artifact, referred to as the matrix ansatz. In this project, we explore a new perspective on the ASEP, based on the relationship between its matrix ansatz and noncommutative infinite-dimensional phenomena. In this manner, we aim to transform the interface between the 'classical' and noncommutative probability theories, arrive at a more fundamental understanding of the ASEP, and open up innovative approaches to a long-standing open question of mathematical analysis, the free group factors isomorphism problem.
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Key Findings |
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Potential use in non-academic contexts |
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Impacts |
Description |
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Summary |
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Date Materialised |
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Sectors submitted by the Researcher |
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.lancs.ac.uk |