Random geometric structures
Many models arising from statistical physics, chemistry, biology and
computer science have a common mathematical theory. We will start by
learning about random walks and their connections to the harmonic
measure, harmonic analysis and spectral theory. We will discuss
the scaling limit of random walk, called Brownian motion, and its
invariance under conformal maps on the complex plain. We will move
on to define different geometric processes such as the random first
passage percolation metric, diffusion limited aggregation, Eden model
and Richardsonâ€™s model, and analyze them using tools from probability
theory and deep connections to other mathematical disciplines.
Prerequisites: Math 411, Math 607.