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 combinatorial 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.
Dipartimento di Fisica, University of Milan and INFN, via Celoria 16, I-20133 Milan, Italy.
Sergio
S
Caracciolo
Dipartimento di Fisica "E. Fermi," University of Pisa and INFN, Largo Bruno Pontecorvo, 3, I-56127 Pisa, Italy.
Gabriele
G
Sicuro