Random Periodic Orbits and Periodic Measures in Interacting Particle Systems
Periodicity refers to the tendency to recur at intervals or the system tends to repeat itself regularly, while randomness refers to uncertainty that cannot easily be captured and may hinder our ability to make a reliable prediction about the future. The concepts of randomness and periodicities do not seem to match well in nature. However, most of the periodic-like phenomena are more or less subject to some form of randomness. For example, the price of wheat in the financial market shows a combined effect of both periodicity and randomness. The intrinsic seasonality of wheat growth suggests the periodicity of the price should follow the change of seasons. The strike price, however, is influenced by not only the real-time supplies and demands but also trading reactions in the international market.
In this project, we will extend the existing analysis framework of studying random periodic behaviour and its periodic measure of random dynamical systems to interacting particle systems (IPS).
Examples of IPS exist within all areas of natural and social sciences, such as traffic flow on highways, pedestrians or constituents of a cellular network, opinion dynamics, the spread of epidemics or fires, reaction-diffusion systems, crystal surface growth, chemotaxis, etc.
Understanding the long-time behaviour of orbits of such complex irreversible systems may help us in effectively predicting the system’s future, its equilibrium states and convergence properties such as existence or absence of dynamical ergodicity for example using methods like entropy production.
Owing to the fundamental nature of dynamical behaviours in IPS, we foresee a multifaceted impact in sustainability applications. IPS is used to model interacting motions in a random environment, such as economics, or the spread of COVID. The analysis of periodic measures for concrete examples like economics will allow us to identify in advance the high likelihood of recession especially during covid pandemics.
“The Tandem Fellowship bridges our research areas. The initial in-person discussion between my research partner and me in Germany is very fruitful, with more ideas for this collaboration.“
Yue is a lecturer from the Department of Mathematics and Statistics, University of Strathclyde, the co-organiser of the Turing Data Science for Mental Health interest group, and the co-founder for OxCOVID19 Database. Prior to joining Strathclyde this January, Yue was a postdoc working on the rough path theory, signature features, and its applications in data science supervised by Professor Terry Lyon FRS at the University of Oxford, and a visiting researcher at Alan Turing Institute.
Benedikt is a professor for applied probability theory at Tu Braunschweig. His research interests lie in the modelling and analysis of systems of many interacting random components that are spatially embedded. Those systems describe phenomena from physics, like liquid-vapour phase transitions, spatial epidemiology of communicable diseases, or peer-to-peer telecommunication in an urban environment. The goal is to derive and describe macroscopic states from highly complex microscopic system configurations. For this he uses mathematical tools from statistical mechanics such as large-deviation theory and stochastic geometry to establish rigorous results. His work is sometimes supported by the comparison with real-world data and by computer simulations. It is presented to an international mathematical audience and researchers from related fields like engineering, life science and materials science.