Finite-size corrections to the spectrum of regular random graphs: An analytical solution.
Finite-size corrections to the spectrum of regular random graphs: An analytical solution.
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对规则随机图谱的有限尺寸修正：解析解。
DOI：
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发表时间：
2014
期刊：
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通讯作者：
Luca Leuzzi
中科院分区：
文献类型：
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作者：
Fernando L. Metz;Giorgio Parisi;Luca Leuzzi
我们对具有 N→∞ 节点的正则随机图谱的 O(1/N) 校正进行了全面的分析研究。解析器的有限大小波动以来自所有可能长度的循环的贡献的加权级数给出，从中我们获得孤立的特征值以及对频谱的连续部分进行 O(1/N) 校正的解析表达式。该解析公式与直接对角化结果之间的比较表现出极好的一致性，证实了我们表达式的正确性。
We develop a thorough analytical study of the O(1/N) correction to the spectrum of regular random graphs with N→∞ nodes. The finite-size fluctuations of the resolvent are given in terms of a weighted series over the contributions coming from loops of all possible lengths, from which we obtain the isolated eigenvalue as well as an analytical expression for the O(1/N) correction to the continuous part of the spectrum. The comparison between this analytical formula and direct diagonalization results exhibits an excellent agreement, confirming the correctness of our expression.