12:15-13:00

Buffet Lunch

13:05

Welcome

13:10 – 13:55

Rosemary Harris (QMUL)
Current fluctuations in interacting particle systems.

I will give an overview of some recent results on current fluctuations in stochastic particle systems. In particular, I will discuss the calculation of large deviation rate functions, the observation of the Gallavotti-Cohen fluctuation symmetry and its breakdown in systems with unbounded state space. In addition, I will present work on the effect of long-range memory on the current large deviation principle, and briefly discuss possible applications and future directions.

14:00 – 14:25

Moez Draief (Imperial)
Interacting particles on random graphs.

We study properties of multiple random walks on a graph under various assumptions of interaction between the particles. These settings correspond to models of graph exploration, epidemic spreading and information dissemination. To simplify the analysis, we will focus on the particular case of random regular graphs.

14:30 – 14:55

Peter Sollich (King’s)
Kinetically constrained glass models.

I will give an overview of some recent work on particle/spin models with kinetic constraints, which can capture many qualitative features of the slow dynamics in “glassy” systems. Surprising results include negative responses to applied fields during aging, and the existence of dynamical phase transitions. These can be understood using mappings to field theories, and exact solutions in d=1.

15:00

Tea

15:30 – 16:15

Martin R. Evans (Edinburgh)
Real-space condensation in interacting particle systems.

In this talk I shall review the phenomenon of real-space condensation wherein a finite fraction of interacting particles moving on a lattice condense onto a single site. The phenomenon has manifestations in a number of complex systems e.g. clustering in granular systems and wealth condensation in macroeconomies. The phenomenon can be understood by considering models with particularly simple stationary states which have a factorised form. To this end I shall review necessary and sufficient conditions for factorised stationary states in a simple class of models. Then the condensation can be analysed and understood in terms of large deviations of sums of random variables and extreme value statistics. Finally I shall consider generalisations such as multiple condensates and entropy driven condensation in systems of polydisperse hard spheres.

16:20 – 16:45

Hubert Fonteijn (UCL)
Monte Carlo models of diffusion in biological tissue and their inversion.

Diffusion-weighted MRI has received a lot of interest because of its ability to elucidate the microstructure of biological tissue, using in-vivo MRI measurements. Current analytic descriptions of diffusion in for instance brain white matter are appealing because of their simplicity, but require a number of simplifying assumptions. Monte Carlo simulations of diffusion in biologically realistic substrates offer an alternative to these analytic descriptions, but are generally considered to be non-invertable. In this talk, we will explore Monte Carlo simulations of diffusion in white matter substrates and we will develop a framework in which these simulations can be inverted using non-linear regression techniques. We will furthermore show that, using this inversion framework, we can derive microstructure parameters from diffusion characteristics of the extracellular compartment.

16:50 – 17:15

Greg Pavliotis (Imperial)
Asymptotic analysis for non-Mark ovian Langevin equations.

In this talk I will present some recent results on qualitative properties of solutions to the generalized Langevin equation (GLE), in a periodic or a confining potential. I will consider a class of quasi-Markovian GLEs, which are obtained from a “distinguished particle coupled to heat bath” model, after elimination of the heat bath variables. Exponentially fast convergence to equilibrium, a homogenization theorem (invariance principle), short time asymptotics and the Markovian limit are studied. Our proofs are based on a careful analysis of a hypoelliptic operator, the generator of an auxiliary Markov process, and systematic use of the recently developed theory of hypocoercivity is made.

17 :20

Wine and snacks