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.