Fluctuations of functions of sparse Erdős-Rényi graphs
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909889501069312 |
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| author | Chu, Hok-Yin |
| author_facet | Chu, Hok-Yin |
| contents | Let $A$ be the (rescaled) adjacency matrix of the Erdős-Rényi graphs $\cal G(N,p)$. For $N^{-1+τ} \leqslant p\leqslant N^{-τ}$, we study the fluctuation of $f(A)_{ii}$ on the global and mesoscopic spectral scales. We show that the distribution of $f(A)_{ii}$ is asymptotically the sum of two independent Gaussian random variables on different scales, where a phase transition occurs on the spectral scale $p$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_03914 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fluctuations of functions of sparse Erdős-Rényi graphs Chu, Hok-Yin Probability 60B20 (Primary) 05C80 (Secondary) Let $A$ be the (rescaled) adjacency matrix of the Erdős-Rényi graphs $\cal G(N,p)$. For $N^{-1+τ} \leqslant p\leqslant N^{-τ}$, we study the fluctuation of $f(A)_{ii}$ on the global and mesoscopic spectral scales. We show that the distribution of $f(A)_{ii}$ is asymptotically the sum of two independent Gaussian random variables on different scales, where a phase transition occurs on the spectral scale $p$. |
| title | Fluctuations of functions of sparse Erdős-Rényi graphs |
| topic | Probability 60B20 (Primary) 05C80 (Secondary) |
| url | https://arxiv.org/abs/2511.03914 |