In order to make any concrete statements about the number of nonzero elements in X, it is necessary to make some assumptions about the distribution of word co-occurrences.
we will assume that the number of co-occurrences of word i with word j, X i j , can be modeled as a power-law function of the frequency rank of that word pair, r i j : The total number of words in the corpus is proportional to the sum over all elements of the cooccurrence matrix X, where we have rewritten the last sum in terms of the generalized harmonic number H n, m .