In a random model of minimum cost bipartite matching based on exponentially distributed edge costs, we show that the distribution of the cost of the optimal solution can be computed efficiently. The distribution is represented by its moment generating function, which in this model is always a rational function. The complex zeros of this function are of interest as the lack of zeros near the origin indicates a certain regularity of the distribution. We propose a conjecture according to which these moment generating functions never have complex zeros of smaller modulus than their first pole. For minimum cost perfect matching, also known as the assignment problem, such a zero-free disk would imply a Gaussian scaling limit.

翻译：在基于指数分布边成本的随机最小成本二部图匹配模型中，我们证明了最优解的成本分布可以被高效计算。该分布通过其矩生成函数表示，在此模型中该函数总为有理函数。该函数的复零点具有研究价值，因为原点附近零点的缺失反映了分布的特定规律性。我们提出一个猜想：这些矩生成函数的复零点模长始终不小于其第一极点的模长。对于最小成本完美匹配问题（即分配问题），此类无零点圆盘的存在将意味着高斯尺度极限的存在。