  Construct recursively a long string of words w1. .. wn, such that at each
step k, w k+1 is a new word with a fixed probability p $\in$ (0, 1), and
repeats some preceding word with complementary probability 1 -- p. More
precisely, given a repetition occurs, w k+1 repeats the j-th word with
probability proportional to j $\alpha$ for j = 1,. .. , k. We show that the
proportion of distinct words occurring exactly times converges as the length n
of the string goes to infinity to some probability mass function in the
variable $\ge$ 1, whose tail decays as a power function when 1 -- p >
$\alpha$/(1 + $\alpha$), and exponentially fast when 1 -- p < $\alpha$/(1 +
$\alpha$).

Probability