稀疏随机矩阵的谱
Spectra of Sparse Random Matrices
摘要：
我们计算的频谱密度合奏稀疏对称随机矩阵使用副本，设法规避困难，遇到了在早期的方法沿罗杰斯和布雷的开创性论文中首次提出的路线。对本地化问题给予了应有的重视。我们的方法并不局限于矩阵上定义的图泊松度分布。定义在正则随机图或无标度图上的矩阵很容易处理。我们还研究了具有行约束的矩阵，如离散图拉普拉斯算子。我们的方法自然地允许展开的总密度的状态到来自不同的本地协调的顶点的贡献。
英文摘要：
We compute the spectral density for ensembles of of sparse symmetric random matrices using replica, managing to circumvent difficulties that have been encountered in earlier approaches along the lines first suggested in a seminal paper by Rodgers and Bray. Due attention is payed to the issue of localization. Our approach is not restricted to matrices defined on graphs with Poissonian degree distribution. Matrices defined on regular random graphs or on scale-free graphs, are easily handled. We also look at matrices with row constraints such as discrete graph Laplacians. Our approach naturally allows to unfold the total density of states into contributions coming from vertices of different local coordination.
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