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...
IntroductionMatrix models are ubiquitous both in Mathematics and in Theoretical Physics. The aim of this course is to introduce the main approaches to U(N)-invariant random matrix models: Coulomb gas, orthogonal polynomials, loop equations, topological recursion, tau-functions and integrable hierarchies. Most of these techniques are based on the fact that the eigenvalues of the random matrix be...