ASYMPTOTICS FOR THE EUCLIDEAN TSP WITH POWER WEIGHTED EDGES

Let U-1,..., U-n denote i.i.d. random variables with the uniform distribution on [0, 1](2), and let T-2:= T-2(U-1,...,U-n) denote the shortest tour through UI,...,U, with square-weighted edges. By drawing on the quasi-additive structure of T-2 and the boundary rooted dual process, it is shown that lim(n-->infinity) IET(2)(U-1,..., U-n) = beta for some finite constant beta.