Sparse Random Matrices and Statistics of Rooted Trees
概率论
2014-11-18 v1 组合数学
谱理论
摘要
We consider the ensemble of N-dimensional random symmetric matrices A that have, in average, p non-zero elements per row. We study the asymptotic behavior of the norm of A in the limit of infinitely increasing N and p. We prove that the value p= log N is the critical one for the norm to be either bounded or not. The arguments are based on the calculus of the tree-type graphs. Asymptotic properties of sparse random matrices essentially depend on the typical degree of a tree vertex that we show to be finite.
引用
@article{arxiv.math/9905015,
title = {Sparse Random Matrices and Statistics of Rooted Trees},
author = {A. Khorunzhy},
journal= {arXiv preprint arXiv:math/9905015},
year = {2014}
}
备注
LaTeX, 19 pages