Sharp Bounds for Sums Associated to Graphs of Matrices

关于可对称化矩阵的Nahm和的注记

Remarks on Nahm sums for symmetrizable matrices

本文将Nahm猜想中对称正定矩阵情形下的一个结论推广到可对称化矩阵，证明其模性对应Bloch群元素为挠元，研究了径向渐近性并给出数值候选列表。

矩阵和的尖锐集中性通过通用性实现

Sharp concentration for sums of matrices with Markovian dependence through universality

本文证明了由ψ-混合马尔可夫链生成的随机矩阵和具有与高斯矩阵相似的谱性质，结合高斯文献的最新进展，实现了尖锐的集中不等式。通过示例展示了其在Wigner型矩阵中的多项式维数改进及谱聚类模型的极限值恢复。

Connes' embedding conjecture and sums of hermitian squares

We show that Connes' embedding conjecture on von Neumann algebras is equivalent to the existence of certain algebraic certificates for a polynomial in noncommuting variables to satisfy the following nonnegativity condition: The trace is nonnegative whenever self-adjoint contraction matrices of the same size are substituted for the variables. These algebraic certificates involve sums of hermitian squares and commutators. We prove that they always exist for a similar nonnegativity condition where elements of separable II_1-factors are considered instead of matrices. Under the presence of Connes'…

与大型随机椭圆矩阵相关的拉普拉斯矩阵的谱

Spectrum of Laplacian matrices associated with large random elliptic matrices

本研究探讨随机椭圆矩阵构造的拉普拉斯矩阵的极限特征值分布，证明其经验谱分布随矩阵规模趋于无穷时收敛到确定性分布，且极限测度可表示为椭圆算子与自由独立高斯正规算子和的Brown测度。

黎曼流形上随机游走导出的加权张量和函数的尾部界

Tail Bounds for Functions of Weighted Tensor Sums Derived from Random Walks on Riemannian Manifolds

本文利用Mond-Pecaric方法建立新张量不等式，并结合Laplace-Beltrami算子谱信息，为流形上随机游走导出的加权张量和给出新的尾部界及转移矩阵列和估计。