Sparse random matrices; Spectral edge and statistics of rooted trees (Q2726720)
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scientific article; zbMATH DE number 1621396
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Sparse random matrices; Spectral edge and statistics of rooted trees |
scientific article; zbMATH DE number 1621396 |
Statements
12 February 2002
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sparse random matrices
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spectral norm
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universality conjecture
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enumeration of trees
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spectral edge
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Erdős-Renyi partial sum
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rooted trees
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high moments
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Erdős-Renyi limit theorem
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large random graph
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Sparse random matrices; Spectral edge and statistics of rooted trees (English)
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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.
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