Asymptotics of correlators of sparse bipartite random graphs
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arXiv
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| Format: | Preprint |
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2019
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| _version_ | 1866918119505657856 |
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| author | Vengerovsky, Valentin |
| author_facet | Vengerovsky, Valentin |
| contents | We study asymptotic behaviour of the correlation functions of bipartite sparse random $N\times N$ matrices. We assume that the graphs have $N$ vertices, the ratio of parts is $\displaystyle\fracα{1-α}$ and the average number of edges attached to one vertex is $α\cdot p$ or $(1-α)\cdot p$. To each edge of the graph $e_{ij}$ we assign a weight given by a random variable $a_{ij}$ with all moments finite. It is shown that the main term of the correlation function of $k$-th and $m$-th moments of the integrated density of states is $N^{-1}n_{k,m}$. The closed system of recurrent relations for coefficients $\{n_{k,m}\}_{k,m=1}^\infty$ was obtained. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1911_10580 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Asymptotics of correlators of sparse bipartite random graphs Vengerovsky, Valentin Mathematical Physics 60B20, 15B52 We study asymptotic behaviour of the correlation functions of bipartite sparse random $N\times N$ matrices. We assume that the graphs have $N$ vertices, the ratio of parts is $\displaystyle\fracα{1-α}$ and the average number of edges attached to one vertex is $α\cdot p$ or $(1-α)\cdot p$. To each edge of the graph $e_{ij}$ we assign a weight given by a random variable $a_{ij}$ with all moments finite. It is shown that the main term of the correlation function of $k$-th and $m$-th moments of the integrated density of states is $N^{-1}n_{k,m}$. The closed system of recurrent relations for coefficients $\{n_{k,m}\}_{k,m=1}^\infty$ was obtained. |
| title | Asymptotics of correlators of sparse bipartite random graphs |
| topic | Mathematical Physics 60B20, 15B52 |
| url | https://arxiv.org/abs/1911.10580 |