Fluctuations in non-Markovian stochastic particle systems

The School of Mathematical Sciences of Queen Mary University of London invite applications for a PhD project commencing either in September 2016 (funded students) or at any point in the academic year (self-funded students).

The emergence of large-scale, macroscopic behaviour of stochastic interacting particle systems (IPS) is a fundamental problem of applied probability, statistical physics, and the theory of complex systems. In the last 20 years or so, considerable progress on this problem has been achieved by studying models of IPS that evolve in a Markovian/memoryless way, such as the asymmetric simple exclusion process (ASEP) or the zero- range process (ZRP). With these models, it has been possible to understand how different interactions between particles give rise to different stationary states and phase transitions, and how the introduction of forces, fields or boundary conditions (e.g., particle reservoirs) in a system determine its nonequilibrium stationary state and the dynamical fluctuations around this state. The PhD project will be concerned with extension of these studies into the relatively new area of non-Markovian IPS, whose evolution depends on the history of the system rather than just its present state in time.

In particular, the focus is likely to be on spatio-temporal fluctuations around the typical behaviour, as formulated in terms of large deviation theory. The study of fluctuations is known to play a fundamental role in revealing symmetry properties of nonequilibrium systems under the reversal of time, notably the so-called “fluctuation relation” which holds for currents or other entropy-related quantities. There are many open theoretical questions for an interested student but there are also possibilities to work on developing efficient numerical algorithms or modelling real-life systems with memory. Potential interdisciplinary projects here could build on existing collaborations with biophysicists at the Universitat des Saarlandes and economists at the University of Sheffield.

This project will be supervised by Dr Rosemary Harris

Full details can be found in the project abstract: http://www.maths.qmul.ac.uk/sites/default/files/phd%20projects%202015/DSSP/harris-2.pdf

The application procedure is described on the School website. For further enquiries please contact Dr Rosemary Harris ([Email Address Removed]).

The deadline for applications to undertake this as a funded project is January 31st, 2016.

This project is eligible for several sources of full funding for the 2016/17 academic year, including support for 3.5 years’ study, additional funds for conference and research visits and funding for relevant IT needs. Applicants interested in the full funding will have to participate in a highly competitive selection process. The best candidates will be eligible to receive a prestigious Ian Macdonald Postgraduate Award of £1000, for which you will be considered alongside your application. The application deadline for full funding is January 31st 2016.

There is also 50% funding scheme available for students who are able to find the matching 50 % of the cost of their studies. Competition for these half-funded slots will be less intensive, and eligible students should mention their willingness to be considered for them in their application. The application deadline for 50 % funding is January 31st 2016.

This project can be also undertaken as a self-funded project, either through your own funds or through a body external to Queen Mary University of London. Self-funded applications are accepted year-round.