Quenched Multiscale Renormalization

Augusto Teixeira

In this series of lectures, we will explain how to use renomalization techniques to establish the existence of phase transitions in stochastic processes. This technique has passed the test of time and proved itself to be very robust and versatile with respect to changes in the underlying model. After explaining the basics of the technique, we will dig into the details of one of its variations (here nicknamed Quenched Multiscale Renormalization), which is able to deal with stochastic processes on random environments. Using this technique we are going to give a beautiful proof of a classical result for Percolation on Stretched Lattices.

These lectures are based in a series of joint works with Hilario, Sa and Sanchis.