Properties of redistricting Markov chains (Sarah Cannon, CMC)

Markov chains have become widely-used to generate random political districting plans. These random districting plans can be used to form a baseline for comparison, and any proposed districting plans that differ significantly from this baseline can be flagged as potentially gerrymandered. However, very little is rigorously known about these Markov chains – Are they irreducible? What is their mixing time? For some, even the stationary distribution remains unknown. I will present recent work that answers some of these questions, which uses tools from probability, computational geometry, and more.