论文标题
循环单调和单调独立性的矩阵模型
Matrix models for cyclic monotone and monotone independences
论文作者
论文摘要
循环单调独立性是非共同独立性的代数概念，在研究级别较小的多矩阵随机矩阵模型的研究中引入了。事实证明，其代数形式非常接近单调独立性，这就是为什么它被命名为环状单调独立性的原因。本文通过表明相同的随机矩阵模型也是单调收敛具有适当选择的状态的模型来概念化这一概念。该观察结果为两种单调独立性提供了统一的非随机矩阵模型。
Cyclic monotone independence is an algebraic notion of noncommutative independence, introduced in the study of multi-matrix random matrix models with small rank. Its algebraic form turns out to be surprisingly close to monotone independence, which is why it was named cyclic monotone independence. This paper conceptualizes this notion by showing that the same random matrix model is also a model for the monotone convergence with an appropriately chosen state. This observation provides a unified nonrandom matrix model for both types of monotone independences.
