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An easy proof of the $\zeta(2)$ limit in the random assignment problem

   
@article{ECP1475,
	author = {Johan Wästlund},
	title = {An easy proof of the $\zeta(2)$ limit in the random assignment problem},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {14},
	year = {2009},
	keywords = {minimum, matching, graph, exponential},
	abstract = {The edges of the complete bipartite graph $K_{n,n}$ are given independent exponentially distributed costs. Let $C_n$ be the minimum total cost of a perfect matching. It was conjectured by M. Mézard and G. Parisi in 1985, and proved by D. Aldous in 2000, that $C_n$ converges in probability to $\pi^2/6$. We give a short proof of this fact, consisting of a proof of the exact formula $1 + 1/4 + 1/9 + \dots + 1/n^2$ for the expectation of $C_n$, and a $O(1/n)$ bound on the variance.},
	pages = {no. 26, 261-269},
	issn = {1083-589X},
	doi = {10.1214/ECP.v14-1475},    
        url = {http://ecp.ejpecp.org/article/view/1475}}