EPSRC logo

Details of Grant 

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:
Texas A and M University University of Strathclyde University of Toulouse III Paul Sabatier
Department: Mathematics and Statistics
Organisation: Lancaster University
Scheme: Standard Research - NR1
Starts: 31 July 2021 Ends: 30 July 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