Report
Spectral gap and embedded trees for the Laplacian of the Erd\H{o}s-R\'enyi graph
| العنوان: | Spectral gap and embedded trees for the Laplacian of the Erd\H{o}s-R\'enyi graph |
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| المؤلفون: | Ducatez, Raphael, Rivier, Renaud |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Probability |
| الوصف: | For the Erd\H{o}s-R\'enyi graph of size $N$ with mean degree $(1+o(1))\frac{\log N}{t+1}\leq d\leq(1-o(1))\frac{\log N}{t}$ where $t\in\mathbb{N}^{*}$, with high probability the smallest non zero eigenvalue of the Laplacian is equal to $2-2\cos(\pi(2t+1)^{-1})+o(1)$. This eigenvalue arises from a small subgraph isomorphic to a line of size $t$ linked to the giant connected component by only one edge. Comment: 22 pages, 4 figures |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2309.17292 |
| رقم الانضمام: | edsarx.2309.17292 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |