EPSRC Reference: 
EP/V048902/1 
Title: 
Noncommutative statistical mechanics: probability at the confluence 
Principal Investigator: 
Blitvic, Dr N 
Other Investigators: 

Researcher CoInvestigators: 

Project Partners: 

Department: 
Mathematics and Statistics 
Organisation: 
Lancaster University 
Scheme: 
Standard Research  NR1 
Starts: 
31 July 2021 
Ends: 
31 August 2022 
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 wideranging applications, from traffic and fluid flow to biological processes. However, recent advances, particularly the emerging parallelism between ASEPtype processes and wellknown 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 infinitedimensional 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 longstanding open question of mathematical analysis, the free group factors isomorphism problem.

Key Findings 
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Potential use in nonacademic contexts 
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Impacts 
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Summary 

Date Materialised 


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Project URL: 

Further Information: 

Organisation Website: 
http://www.lancs.ac.uk 