Co-authors: Michael Damron (Indiana University), Jack T. Hanson (Indiana University)
For a subadditive ergodic sequence Xm,n, Kingman's theorem gives convergence for the terms X0,n/n to some non-random number g. In this talk, I will discuss the convergence rate of the mean EX0,n/n to g. This rate turns out to be related to the size of the random fluctuations of X0,n; that is, the variance of X0,n, and the main theorems I will present give a lower bound on the convergence rate in terms of a variance exponent. The main assumptions are that the sequence is not diffusive (the variance does not grow linearly) and that it has a weak dependence structure. Various examples, including first and last passage percolation, bin packing, and longest common subsequence fall into this class. This is joint work with Michael Damron and Jack Hanson.
view more