Theory and Applications of Interacting Particle Systems

Lead CIs: Jan de Gier and Peter Forrester

Fundamental models of interacting particles, such as those occurring in mathematical physics and queuing theory, are widely studied to understand non-equilibrium behavior in physical systems consisting of large numbers of particles, to study large classes of transport phenomena, scheduling mechanisms and interface growth. This project combines theoretical approaches with computational and statistical analysis.

The theoretical part of the project will aim to derive exact analytical expressions for properties encoding emerging and collective behaviour from microscopic principles. Such properties include important stationary and dynamical properties of model systems such as exclusion processes and queuing systems. Tools to be used and further developed lie in the realm of stochastic calculus, queuing theory, integrable probability, and include matrix product states and random matrix theory.

The applied part of this project will involve computer simulations of large networks of interacting agents to model urban traffic on networks. This part of the project will also involve validation and calibration of simulated data to real world data provided by industry partner VicRoads.