可解的随机分块三对角矩阵族
Solvable Families of Random Block Tridiagonal Matrices
AI总结：
本文引入两类随机三对角块矩阵，其联合特征值分布可显式计算，揭示了超越典型平均场对数气体类型的特征值相互作用。通过矩阵模型，描述了谱边缘的点过程极限，涉及随机微分算子和耦合扩散系统。
摘要：
我们引入两类随机三对角块矩阵，其联合特征值分布可显式计算。这些分布是随机矩阵理论中的新发现，展示了超越典型平均场对数气体类型的特征值相互作用。利用这些矩阵模型，我们通过某些随机微分算子以及耦合的扩散系统两种方式描述了谱边缘的点过程极限。在此过程中，我们建立了若干涉及Vandermonde行列式乘积和的代数恒等式。
英文摘要：
We introduce two families of random tridiagonal block matrices for which the joint eigenvalue distributions can be computed explicitly. These distributions are novel within random matrix theory, and exhibit interactions among eigenvalue coordinates beyond the typical mean-field log-gas type. Leveraging the matrix models, we go on to describe the point process limits at the edges of the spectrum in two ways: through certain random differential operators, and also in terms of coupled systems of diffusions. Along the way we establish several algebraic identities involving sums of Vandermonde determinant products.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
