Seminar

Abstract:  I will consider a Markov process on a system of interlacing particles that is placed on the grid $\Z \times \N$. Each particle has an exponential clock and when the clock rings it attempts to jump to the right by one, but the jump is subject to rules that respect the interlacing condition. There are two types of particles, one with a low jump rate and the other with a high jump rate. After large time a surface emerges that describes the limiting behavior of the system at the macroscopic scale. Due to the different jump rates the normal to the surface has a jump. Despite this discontinuity the fluctuations around the limiting surface are governed by the Gaussian free field.