Dr Codina Cotar awarded £98k EPSRC First Grant to study Continuous Gradient Models
23 March 2015
Dr Codina Cotar has been awarded the EPSRC Grant EP/M027694/1 under the First Grant Scheme. The project is called “Continuous gradient interfaces with disorder”.
Continuous gradient models are natural generalizations to higher d-dimensional time of the standard random walk and have drawn a lot of attention lately. Partly, this is due to the fact that the contour lines of their interface height converge in d=2 to Schramm's SLE - a family of random planar curves shown to be the universal scaling limit of many important two-dimensional lattice models in probability and statistical mechanics (2006 Fields Medal for Wendelin Werner). Moreover, gradient models are connected to random interlacements, a novel probability area pioneered by Sznitman, to reinforced random walks, and to Liouville quantum gravity. The classic gradient model assumes a smooth medium, i.e. without disorder. However, most phenomena in nature exhibit some disorder due to impurities entering the systems or to materials which have defects or inhomogeneities.
In this proposal, we will mainly explore the effects of disorder on continuous gradient models which is an almost unchartered territory mathematically. I will seek to answer questions such as whether the addition of a small amount of disorder modifies the nature of the phase transitions of the underlying homogeneous gradient model, i.e. if disorder is relevant, I will aim to identify non-standard phase transitions, to find new instances of universality behaviour, and to create connections between gradients and other models with disorder by taking questions from d=1 (polymers) to the next level d>1 (gradients), e.g. quenched vs annealed free energy.
The total amount awarded was £98,386 and will fund a postdoctoral researcher for 12 months.