We consider the problem of minimizing cost among one-to-one assignments of$n$ jobs onto $n$ machines. The random assignment problem refers to the casewhen the cost associated with performing jobs on machines are random variables.Aldous established the expected value of the smallest cost, $A_n$, in thelimiting $n$ regime. However the distribution of the minimum cost has not beenestablished yet. In this paper we conjecture some distributional properties ofmatchings in matrices. If this conjecture is proved, this will establish that$\sqrt{n}(A_n - E(A_n)) \overset{w}{\Rightarrow} N(0,2)$. We also establish thelimiting distribution for a special case of the Random Assignment Problem.
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机译：我们考虑将$ n $作业一对一分配到$ n $机器上的成本最小化的问题。随机分配问题是指与在计算机上执行作业相关的成本是随机变量的情况.Aldous在限制$ n $体制中确定了最小成本$ A_n $的期望值。但是，尚未确定最低成本的分配。在本文中，我们推测矩阵中匹配的一些分布特性。如果证明了这一猜想，则将确定$ \ sqrt {n}（A_n-E（A_n））\ overset {w} {\ Rightarrow} N（0,2）$。我们还为随机分配问题的特殊情况建立了极限分布。
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