Asymptotic independence of maximum waiting times for increasing alphabet (Q1203462)

Let \({\mathcal X}\) be a finite alphabet of size \(n\). Consider the waiting time until each pattern of length \(k\) \((k\geq 1)\) over a fixed alphabet of size \(n\) appears at least once in an infinite sequence of independent uniformly distributed random letters. The aim of this paper is to determine the limiting finite-dimensional joint distributions of these waiting times after suitable normalization and provide an estimate for the rate of convergence. Finally it is shown that these waiting times are getting independent.