Description: The central-limit type results are universal in many random walk models: they are known as Donsker’s theorem for the classical Zd random walk, and also hold for some random walks in random environment, even when the environment is degenerate like percolation. In their proofs, the homogenization theory, which comes from PDE, plays an important role. This course will cover the follo...
AbstractIn this talk, we will discuss the behavior of the separating systole for random hyperbolic surfaces with respect to the Weil-Petersson measure of the moduli space. We show that its length is approximately 2log(g)-4log(log(g)) and it separates out a one-holed torus for generic surfaces. Some other geometric quantities are also considered. This talk is based on joint works with Xin Nie, H...