We discuss the process convergence of the time dependent fluctuations of linear eigenvalue statistics of random circulant matrices with independent Brownian motion entries, as the dimension of the matrix tends to ∞. Our derivation is based on the trace formula of circulant matrix, method of moments and some combinatorial techniques.

中文翻译：

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随机循环矩阵线性特征值统计波动的过程收敛

我们讨论了具有独立布朗运动条目的随机循环矩阵的线性特征值统计的时间相关波动的过程收敛，因为矩阵的维数趋于∞. 我们的推导是基于循环矩阵的迹公式、矩量法和一些组合技术。