On the Fluctuations of the Stochastic Traveling Salesperson Problem

Consider n points X1, ', Xn independently and uniformly distributed on the unit square [0, 1]2. Denote by Tn the length of the shortest tour through X1, ', Xn. We prove that for some universal constant K, we have P|Tn-ETn| ≥ t ≥ K-1 exp-t2K whenever t ≤ K-1n1/2.