  We analyze the expected running time of WalkSAT, a well-known local search
procedure for satisfiability solving, on satisfiable instances of the k-XOR SAT
problem. We obtain estimates of this expected running time by reducing the
problem to a setting amenable to classical techniques from drift analysis.
  A crucial ingredient of this reduction is the definition of (new, explosive)
hypergraph versions of interacting particle systems, notably of coalescing and
annihilating random walks as well as the voter model. The use of these tools
allows to show that the expected running time of WalkSAT depends on structural
parameter (we call odd Cheeger drift) of the dual of the formula hypergraph.
