Branching Random Walks
Sep 15-Oct 13, 2020
ID: 35275142691 Password: 202002
A branching random walk is a process that simultaneously generalizes the concepts of a branching process and of a random walk. It has deep connection with other models coming from mathematical physics and dynamical system, such as the Mandelbrot's multiplicative cascades, the Gaussian free fields in two dimension and more general log-correlated Gaussian fields. In this mini-course, we provide an elementary introduction to the branching random walks on real line, including the spinal decomposition and the asymptotic properties of the extremal positions in the branching random walk. As an application, we consider the critical behavior of the branching random walks on the homogeneous trees. In the last part, we introduce the branching random walk with exponentially decreasing steps and present its connection to the stochastically self-similar measures.