论文标题
非零特征值的统计数据和具有非阴性条目的低级随机矩阵的奇异值
Statistics of the non-zero eigenvalues and singular values of low-rank random matrices with non-negative entries
论文作者
论文摘要
我们通过分析计算非零特征值的总和和产物的概率和矩，以及（i）非负条目，（ii）固定等级的随机矩阵的奇异值，以及（iii）每行条目的规定总和。在马尔可夫连锁店，经济学和社交网络的背景下，讨论了此类矩阵的应用。所有结果在有限基质大小上都是有效的，并且根据一般Dirichlet随机变量的向量的统计数据给出。分析结果通过数值模拟以极好的一致性来证实。
We compute analytically the probability distribution and moments of the sum and product of the non-zero eigenvalues and singular values of random matrices with (i) non-negative entries, (ii) fixed rank, and (iii) prescribed sums of the entries in each row. Applications of such matrices are discussed in the context of Markov chains, economics and social networks to name a few. All results are valid at finite matrix size and are given in terms of the statistics of vectors of general Dirichlet random variables. Analytical results are corroborated by numerical simulations throughout with excellent agreement.
