On the one dimensional Euclidean matching problem: exact solutions,   correlation functions and universality
  We discuss the equivalence relation between the Euclidean bipartite matching problem on the line and on the circumference and the Brownian bridge process on the same domains. The equivalence allows us to compute the correlation function and the optimal cost of the original combinatoric problem in the thermodynamic limit; moreover, we solve also the minimax problem on the line and on the circumference. The properties of the average cost and correlation functions are discussed. 
Sergio Caracciolo and Gabriele Sicuro
cond-mat.dis-nn math-ph math.MP