In recent years political parties have more and more expertly
crafted political districtings to favor one side or another, while at
the same time, entirely new techniques to detect and measure these
efforts are being developed.
I will discuss a rigorous method which uses Markov chains---random
walks---to statistically assess gerrymandering of political districts
without requiring heuristic validation of the structures of the Markov
chains which arise in the redistricting context. In particular, we will
see two examples where this methodology was applied in successful
lawsuits which overturned district maps in Pennsylvania and North Carolina.