Asymptotic Enumeration of Difference Matrices over Cyclic Groups
  We identify a relationship between a certain family of random walks on Euclidean lattices and difference matrices over cyclic groups. We then use the techniques of Fourier analysis to estimate the return probabilities of these random walks, which in turn yields the asymptotic number of difference matrices over cyclic groups as the number of columns increases. 
Aaron M Montgomery
math.CO math.PR