D. Aldous, Asymptotics in the random assignment problem, Probability Theory and Related Fields, vol.8, issue.4, pp.507-534, 1992.
DOI : 10.1007/BF01192719

D. Aldous and A. Bandyopadhyay, A survey of max-type recursive distributional equations, The Annals of Applied Probability, vol.15, issue.2, pp.1047-1110, 2005.
DOI : 10.1214/105051605000000142

D. Aldous and J. M. Steele, The Objective Method: Probabilistic Combinatorial Optimization and Local Weak Convergence, 2003.
DOI : 10.1007/978-3-662-09444-0_1

A. Bandyopadhyay, Bivariate uniqueness in the logistic recursive distributional equation, 2002.

M. Bayati, D. Shah, and M. Sharma, Max-Product for Maximum Weight Matching: Convergence, Correctness, and LP Duality, IEEE Transactions on Information Theory, vol.54, issue.3, 2008.
DOI : 10.1109/TIT.2007.915695

P. Billingsley, Convergence of probability measures, Wiley Series in Probability and Statistics, 1999.
DOI : 10.1002/9780470316962

D. Coppersmith and G. Sorkin, Constructive bounds and exact expectations for the random assignment problem, Random Structures and Algorithms, vol.8, issue.2, pp.113-144, 1999.
DOI : 10.1002/(SICI)1098-2418(199909)15:2<113::AID-RSA1>3.0.CO;2-S

M. E. Dyer, A. M. Frieze, and C. J. Mcdiarmid, On linear programs with random costs, Mathematical Programming, vol.8, issue.1, pp.3-16, 1986.
DOI : 10.1007/BF01589437

J. Edmonds and R. Karp, Theoretical Improvements in Algorithmic Efficiency for Network Flow Problems, Journal of the ACM, vol.19, issue.2, pp.248-264, 1972.
DOI : 10.1145/321694.321699

M. X. Goemans and M. S. Kodialam, A Lower Bound on the Expected Cost of an Optimal Assignment, Mathematics of Operations Research, vol.18, issue.2, pp.267-274, 1993.
DOI : 10.1287/moor.18.2.267

R. M. Karp, An algorithm to solve them ??n assignment problem in expected timeO(mn logn), Networks, vol.1, issue.2, pp.143-152, 1980.
DOI : 10.1002/net.3230100205

A. Lazarus, Certain expected values in the random assignment problem, Operations Research Letters, vol.14, issue.4, pp.207-214, 1993.
DOI : 10.1016/0167-6377(93)90071-N

S. Linusson and J. , A proof of Parisi?s conjecture on the random assignment problem, Probability Theory and Related Fields, vol.128, issue.3, pp.419-440, 2004.
DOI : 10.1007/s00440-003-0308-9

M. Mézard and G. Parisi, On the solution of the random link matching problems, Journal de Physique, vol.48, issue.9, pp.1451-1459, 1987.
DOI : 10.1051/jphys:019870048090145100

C. Nair, B. Prabhakar, and M. Sharma, Proofs of the Parisi and Coppersmith-Sorkin random assignment conjectures, Random Structures and Algorithms, vol.26, issue.4, pp.413-444, 2005.
DOI : 10.1002/rsa.20084

B. Olin, Asymptotic properties of random assignment problems, 1992.

J. Pearl, Probabilistic reasoning in intelligent systems: Networks of plausible inference, 1988.

D. W. Walkup, On the Expected Value of a Random Assignment Problem, SIAM Journal on Computing, vol.8, issue.3, pp.440-442, 1979.
DOI : 10.1137/0208036

J. Yedidia, W. Freeman, and Y. Weiss, Generalized belief propagation, Mitsubishi Elect. Res. Lab, 2000.

A. Appendix, Proof of Lemma 4.1. The proof of Lemma 4.1 lays upon two technical lemmas stated below. Essentially, the picture is the following: when i gets large