Correlations between real and complex zeros of a random polynomial
| Autor: | Götze, Friedrich, Koleda, Denis, Zaporozhets, Dmitry |
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| Rok vydání: | 2016 |
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| Druh dokumentu: | Working Paper |
| Popis: | Consider a random polynomial $$ G(z):=\xi_0+\xi_1z+\dots+\xi_nz^n,\quad z\in\mathbb{C}, $$ where $\xi_0,\xi_1,\dots,\xi_{n}$ are independent real-valued random variables with probability density functions $f_0,\dots,f_n$. We give an explicit formula for the mixed $(k,l)$-correlation function $\rho_{k,l}:\mathbb{R}^k\times\mathbb{C}_+^l \to\mathbb{R}_+$ between $k$ real and $l$ complex zeros of $G_n$. |
| Databáze: | arXiv |
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