An easy proof of the $\zeta(2)$ limit in the random assignment problem
An easy proof of the $\zeta(2)$ limit in the random assignment problem
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 $\pi^2/6$. …