Convergence in Distribution for Best-Fit Decreasing

Consider independent random variables $X_1, \dots, X_n$ uniformly distributed over $[0,1]$, and denote by $B_n$ the number of bins needed to pack items of these sizes using the best fit decreasing algorithm. We prove that the random variable $n^{-1/2}$ converges in distribution to a nonnormal limit. The method consists of showing that the patterns created by the algorithm exhibit some kind of convergence.