Large systems of interacting individuals are central to countless areas of science; the individuals may be people, computers, animals, or particles, and the large systems may be financial markets, networks, flocks, or fluids. Mean field theory was originally developed to study particle systems and has since emerged as the most widespread mathematical foundation for studying a broader class of these systems. The key insight of this approach is that the infinite-population (continuum) limit of the finite population model can effectively approximate macroscopic and statistical features of the system as well as the behaviour of a typical or average particle. The young theory of Mean field game (MFG) studies strategic decision making in very large populations of small interacting individuals (such as the behaviour of the agent in economy or crowd behaviour).
Applications to Smart Grids
The key feature of the smart grids paradigm is that end customers actively participate in the energy market and consequently their strategic behaviour needs to be analysed (see e.g. Bagagiolo and Bauso, 2014)
Applications to Statistical sampling
Diffusion processes provide at the core of many algorithms used in statistics to sample with so-called intractable distributions.