论文标题
某些图案矩阵的线性特征值统计的时间依赖性波动
Time dependent fluctuations of linear eigenvalue statistics of some patterned matrices
论文作者
论文摘要
考虑$ n \ times n $反向循环$ rc_n（t）$和对称循环$ sc_n（t）$矩阵，带有独立的布朗尼运动条目。我们将这些矩阵线性特征值统计的时间依赖性波动的过程收敛为$ n \ tents \ infty $，当统计的测试函数是多项式时。这些证明主要是基于痕量公式，矩的方法和过程收敛的一些结果。
Consider the $n \times n$ reverse circulant $RC_n(t)$ and symmetric circulant $SC_n(t)$ matrices with independent Brownian motion entries. We discuss the process convergence of the time dependent fluctuations of linear eigenvalue statistics of these matrices as $n \tends \infty$, when the test functions of the statistics are polynomials. The proofs are mainly combinatorial, based on the trace formula, method of moments and some results on process convergence.
