Research summary
Random processes play a role in everything from the shuffling of a deck of cards to the spread of a disease to the evolution of genes within a population. These random processes often live in a space within a geometric structure. As Canada Research Chair in Probability, Dr. Mathav Murugan aims to understand how the long-term behaviour of random processes relates to the geometry of the underlying space.
He and his research team are developing robust, widely applicable methods to obtain quantitative estimates of the behaviour of diffusions, random walks, and jump processes, or more generally Markov processes. Markov processes are used to model a wide range of phenomena in physics, biology, statistics and finance. By improving our understanding of the interactions between the behaviour of random processes and their underlying geometry, Murugan’s research will address novel questions at the interface between probability, analysis and geometry.