|DATE||SPEAKER||TITLE (click for abstract below)|
|September 11||Organizational Meeting||Setting Topics for Semester to Come|
|September 18||Nick Bhattacharya||MCMC and Mixing of Markov Chains|
|September 25||No speaker|
|October 2||Satyaki Mukherjee||Couplings for Bounding Mixing Times|
|October 9||Milind Hegde||Lower Bounds on Mixing Times|
Title and Abstracts
We review some basic language about mixing times and stationarity. We also discuss two methods for sampling a distribution using a Markov Chain (known as MCMC) - Glauber Dynamics (also known as Gibbs sampling and the Metropolis chain.
This will be a talk directly out of chapters 3-5 of MCMT.
One technique for bounding mixing times is to pick a good coupling of our given chain with another and follow them until some random time. We focus on two techniques - a special case of what's called a Grand Coupling and selecting Strong Stationary Times. These methods are applied to examples from card shuffling and random walks on graphs.
This talk is from chapters 5 and 6 of MCMT.
Lower bounds on mixing times require a very different technique from upper bounds discussed last week. We outline three methods for finding lower bounds, which require increasingly more information about transition structure of our chain. We provide some examples from card shuffling and random walks - in particular, we show the upper bound of last week's card shuffling example was tight.
This talk is from chapter 7 of MCMT.