Computing the Behaviour of Random Processes
Random processes provide basic modeling and computational tools for a wide range of complex phenomena in physics, biology, computer science, statistics and finance. For instance, random processes are used to analyze heat diffusion on a metallic object, the shuffling of a deck of cards, the spread of a disease, or the evolution of genes in a population.
These random processes often live in a space with a geometric structure. It is, therefore, important to study how the evolution of random processes relates to the geometric features of the underlying space.
Dr. Mathav Murugan is Canada Research Chair in Probability. His research will use ideas from probability theory, differential equations, and geometry to explore such fundamental questions as: Suppose you are given the shape of an object, can you calculate how heat will flow on that object? Conversely, if you are given the behaviour of heat flow on an object, can you assume its shape? Which geometric features of the object are really essential to determine the behaviour of heat diffusion? How do small changes to the shape of an object affect the behaviour of heat diffusion?
The findings from Murugan’s research will improve our understanding of the interplay between the behaviour of random processes and the geometry of the space in which an object lives. He aims to develop new mathematical tools to analyze random processes that occur in various scientific disciplines, and improve upon existing ones.