Limiting empirical spectral distribution for the non-backtracking matrix of an Erdős-Rényi random graph
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2017
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866911742545625088 |
|---|---|
| author | Wang, Ke Wood, Philip Matchett |
| author_facet | Wang, Ke Wood, Philip Matchett |
| contents | In this note, we give a precise description of the limiting empirical spectral distribution (ESD) for the non-backtracking matrices for an Erdős-Rényi graph assuming $np/\log n$ tends to infinity. We show that derandomizing part of the non-backtracking random matrix simplifies the spectrum considerably, and then we use Tao and Vu's replacement principle and the Bauer-Fike theorem to show that the partly derandomized spectrum is, in fact, very close to the original spectrum. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1710_11015 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Limiting empirical spectral distribution for the non-backtracking matrix of an Erdős-Rényi random graph Wang, Ke Wood, Philip Matchett Probability In this note, we give a precise description of the limiting empirical spectral distribution (ESD) for the non-backtracking matrices for an Erdős-Rényi graph assuming $np/\log n$ tends to infinity. We show that derandomizing part of the non-backtracking random matrix simplifies the spectrum considerably, and then we use Tao and Vu's replacement principle and the Bauer-Fike theorem to show that the partly derandomized spectrum is, in fact, very close to the original spectrum. |
| title | Limiting empirical spectral distribution for the non-backtracking matrix of an Erdős-Rényi random graph |
| topic | Probability |
| url | https://arxiv.org/abs/1710.11015 |