Almost sure convergence of the minimum bipartite matching functional in Euclidean space
J. Boutet De Monvel 1, Olivier C. Martin 2 COMBINATORICA 22 (2002) 523-530 Let $L_N = L_{MBM}(X_1,…, X_N; Y_1,…, Y_N)$ be the minimum length of a bipartite matching between two sets of points in $\mathbf{R}^d$, where $X_1,…, X_N,…$ and $Y_1,…, Y_N,…$ are random points independently and uniformly distributed in $[0,1]^d$. We prove that for $d \ge 3$, $L_N/N^{1-1/d}$ converges with […]
