Random Walk Sampling: Examples & Techniques for Bounding Mixing Time 
by Linji Yang 

In this talk I will give an introduction of the Markov Chain Monte Carlo Method, which uses markov chains to oample
interesting combinatorial objects such as proper colorings, independent sets and perfect matchings of a graph. I will
introduce methods such as Couplings and Canonical Paths which have been widely used to analyze how many steps Markov
Chains needs to go (mixing time) in order to get a sufficiently random combinatorial object. I will also give a brief
survey of some recent results in the sampling of colorings.