大图的随机k-提升的谱（k可能很大）
The spectrum of random k-lifts of large graphs (with possibly large k)
摘要：
我们研究了大的随机k-提升，但在其他任意图G。我们证明了提升的邻接矩阵的所有特征值不是G的特征值的阶都是（D ln（kn））^{1/2}，其中D是G的最大度.类似地，也很有可能，提升的拉普拉斯算子的“新”特征值都在长度为（ln（nk）/d）^{1/2}的区间内，其中d是G的最小度。我们还证明，从谱图论的角度来看，有很小的差异之间的随机k_1 k_2.图的k_r-提升和图的随机k_2-提升的随机k_1-提升。一个随机k_r-提升。主要的证明工具是作者最近提出的随机矩阵和的集中不等式。
英文摘要：
We study random k-lifts of large, but otherwise arbitrary graphs G. We prove that, with high probability, all eigenvalues of the adjacency matrix of the lift that are not eigenvalues of G are of the order (D ln (kn))^{1/2}, where D is the maximum degree of G. Similarly, and also with high probability, the "new" eigenvalues of the Laplacian of the lift are all in an interval of length (ln (nk)/d)^{1/2} around 1, where d is the minimum degree of G. We also prove that, from the point of view of Spectral Graph Theory, there is very little difference between a random k_1k_2 ... k_r-lift of a graph and a random k_1-lift of a random k_2-lift of ... of a random k_r-lift of the same graph. The main proof tool is a concentration inequality for sums of random matrices that was recently introduced by the author.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
