AI 中文总结
本文证明了d≥2时全Fock空间上多Toeplitz算子的Szegő第一极限定理，给出截断多Toeplitz算子特征值的极限分布及熵，其与经典d=1情形差异显著，纯原子测度可关联渗流过程。
AI 中文摘要
我们陈述并证明了d≥2个字母的全Fock空间上作用的多Toeplitz算子的Szegő第一极限定理的一个版本。特别地，我们证明了截断多Toeplitz算子的特征值分布收敛到一个极限分布。我们在一些特殊情形下计算了该极限分布及其相关熵。即使在最简单的例子中，该极限分布也与对应d=1的经典情形截然不同；在这些例子中，我们得到了一个纯原子测度，它与一个简单三对角随机矩阵模型相关的渗流过程具有概率解释关联。
英文摘要
We state and prove a version of Szegő's first limit theorem for multi-Toeplitz operators acting in the full Fock space in $d\geq 2$ letters. In particular we show that the eigenvalue distributions of truncated multi-Toeplitz operators converge to a limiting distribution. We compute this limiting distribution and its associated entropy in some special cases. Even in the simplest examples the limiting distribution is quite different from the classical case (corresponding to $d=1$); in these examples we obtain a purely atomic measure, which admits a probabilistic interpretation in connection with a percolation process associated to a simple tridiagonal random matrix model.
