Directed Random Walks on Colored, Periodic Lattices: A Gauge Theoretic   Approach
  We define a random walk problem which admits analytic results, on a class of infinite periodic lattices which are directed and colored. Our approach is motivated from the fact that such lattices arise in string theoretic constructs of certain gauge theories. An operator counting problem in the latter is mapped to a problem in random walks. This is illustrated with several examples. 
Subhash Mahapatra, Prabwal Phukon, Tapobrata Sarkar
cond-mat.stat-mech hep-th