The Zipf law for random texts with unequal letter probabilities and the pascal pyramid

We study a model of generating words with independent unequal probabilities of letters. We prove that the probability p(r) of words of rank r has a power asymptotics. As distinct from a paper published earlier by B. Conrad andM.Mitzenmacher, we give a short proof, using elementary methods, and obtain an explicit formula for the degree of the power law. © Allerton Press, Inc., 2012