Maximizing total variation distance for the Ising model
25/12/2022
Consider Glauber dynamics for the Ising model on a finite graph. Which pair of initial states maximizes the total variation distance at time 
?
Markov chain mixing
The power law for the mixing time of Swendsen-Wang dynamics for the Ising model
25/12/2022
Does Swendsen-Wang dynamics for the Ising model on an 
-vertex graph always mix in time 
?
A Markov chain arising from Gaussian elimination
03/10/2022
Consider a Markov chain on the set of n by n invertible matrices mod 2, where in each step, two distinct rows are chosen uniformly at random, and the first row is added to the second mod 2. How does the mixing time grow with n? And how does it change if only test functions that are computable in polynomial time are allowed?
Catalan mixing
02/10/2022
Consider random transpositions on sequences of 1, -1, with non-negative partial sums (transpositions that violate this condition are rejected.) How does the mixing time of this chain grow as a function of n ?