标题： 随机测度的相互亲和性 显示英文标题

标题： The mutual affinity of random measures

摘要： 我们考虑一个有限事件空间$\Omega$上的概率测度集合。 互惠相似性是通过相关格拉姆矩阵的谱来引入的。 我们证明，对于随机选择的测度，在测度的数量以及$\Omega$的基数趋于无穷大的极限情况下，格拉姆矩阵的经验特征值分布收敛到一个固定分布。 显示英文摘要

摘要： We consider a set of probability measures on a finite event space $\Omega$. The mutual affinity is introduced in terms of the spectrum of the associated Gram matrix. We show that, for randomly chosen measures, the empirical eigenvalue distribution of the Gram matrix converges to a fixed distribution in the limit where the number of measures, together with the cardinality of $\Omega$, goes to infinity.