标题： 关于随机图拉普拉斯矩阵的渐近可解性 显示英文标题

标题： On asymptotic solvability of random graph's laplacians

摘要： 我们观察到，在顶点数N趋于无限大的极限下，随机图G的拉普拉斯算子代表了一个可以显式求解的模型。具体来说，我们推导了图G邻接矩阵的极限平均矩的递推关系。这些关系允许研究相应的特征值分布函数；我们证明其密度具有无限支撑，这与普通离散拉普拉斯算子的情况相反。 显示英文摘要

摘要： We observe that the Laplacian of a random graph G on N vertices represents and explicitly solvable model in the limit of infinitely increasing N. Namely, we derive recurrent relations for the limiting averaged moments of the adjacency matrix of G. These relations allow one to study the corresponding eigenvalue distribution function; we show that its density has an infinite support in contrast to the case of the ordinary discrete Laplacian.