| EPSRC Reference: |
EP/V048902/1 |
| Title: |
Noncommutative statistical mechanics: probability at the confluence |
| Principal Investigator: |
Blitvic, Dr N |
| Other Investigators: |
|
| Researcher Co-Investigators: |
|
| Project Partners: |
|
| Department: |
Mathematics and Statistics |
| Organisation: |
Lancaster University |
| Scheme: |
Standard Research - NR1 |
| Starts: |
31 January 2021 |
Ends: |
30 January 2023 |
Value (£): |
201,866
|
| EPSRC Research Topic Classifications: |
| Logic & Combinatorics |
Mathematical Analysis |
| Statistics & Appl. Probability |
|
|
| EPSRC Industrial Sector Classifications: |
| No relevance to Underpinning Sectors |
|
|
| Related Grants: |
|
| Panel History: |
|
|
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.
|
|
Key Findings |
|
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
|
|
Potential use in non-academic contexts |
|
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
|
|
Impacts |
|
| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
| Summary |
|
| Date Materialised |
|
|
|
|
Sectors submitted by the Researcher |
|
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
|
| Project URL: |
|
| Further Information: |
|
| Organisation Website: |
http://www.lancs.ac.uk |