Details of Grant 

EPSRC Reference:	EP/C540247/1
Title:	Intersection local times and stochastic processes in random media
Principal Investigator:	Morters, Professor P
Other Investigators:
Researcher Co-Investigators:
Project Partners:
Department:	Mathematical Sciences
Organisation:	University of Bath
Scheme:	Advanced Fellowship (Pre-FEC)
Starts:	01 September 2005	Ends:	31 August 2010	Value (£):	330,436
EPSRC Research Topic Classifications:	Mathematical Analysis
EPSRC Industrial Sector Classifications:	No relevance to Underpinning Sectors
Related Grants:
Panel History:	Panel Date Panel Name Outcome 18 Apr 2005 Mathematical Sciences ARF interviews Deferred 14 Mar 2005 Maths Fellowships 2005 Sifting Panel Deferred
Summary on Grant Application Form
Mathematical models of physical phenomena are usually modelled as if taking place in a homogeneous environment. Real materials or substances however often have defects or inhomogeneities, and are therefore better modelled as random. It is therefore very desirable to know, what kind of qualitatively new effects can arise when processes are taking place in a random environment or medium. Unfortunately processes in random media are much more difficult to study than processes in homogeneous media and very often one has to resort to 'simple' toy models, which are mathematically tractable but represent only a small number of features of the original physical problem.The main aspect of the proposed research is to provide a variety of case studies for stochastic processes in random media in an attempt to explore the new behaviour that can emerge from the interaction with the medium. To understand the difficulty in these models it is best to imagine the process as a macroscopic picture emerging from a large number of microscopic (i.e. small) particles moving in space and interacting with the medium. This interaction can take different forms, for example there might be holes in the medium where particles cannot go, or areas where particles can replicate more easily. Initially all particles move independently, but as they may occupy the same locations their interaction with the medium introduces dependence between the particles. For example they might all want to move to a location where the medium is particularly beneficial to their survival, or they might want to avoid traps in the medium, and therefore they stick together much more than in a homogeneous environment. To handle this dependence it is important to measure how much time different particles spend in the same (or approximately the same) location. A quantity which does this is the intersection local time of the system. The project therefore proposes to study intersection local times, for which a range of new approaches has recently been developed. I will make new contributions to the understanding of intersection local times, and then use these techniques to study stochastic processes in random media.
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Organisation Website:	http://www.bath.ac.uk