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Sparse random matrices; Spectral edge and statistics of rooted trees. (English) Zbl 0979.15023

The author applies a graph theory method to study the high moments of sparse random square matrices that have, on average, \(p\) non-zero elements per row. The asymptotic behaviour of the spectral norm is evaluated and it is shown that \(p\) has a critical value such that a certain limit of the spectral norm involving \(p\) is bounded or not. Relations with the Erdős-Renyi limit theorem and properties of large random graph are discussed.

MSC:

15B52 Random matrices (algebraic aspects)
05C05 Trees
05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
15A60 Norms of matrices, numerical range, applications of functional analysis to matrix theory
05C80 Random graphs (graph-theoretic aspects)
60F05 Central limit and other weak theorems
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