Georgia Institute of Technology College of Sciences

In this seminar, I will talk about a few recent developments in the random colorings, random weighted independent sets and other 2-spin models on different classes of graphs such as the square lattices and the triangular free graphs. I will focus on the so-called spatial mixing property of these models and discuss about the consequences (e.g., fast mixing of the Markov chains) of the spatial mixing property as well as the techniques of proving it.