A Refinement of the Central Limit Theorem for Random Determinants
| Autor: | V. L. Girko |
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| Rok vydání: | 1998 |
| Předmět: | |
| Zdroj: | Theory of Probability & Its Applications. 42:121-129 |
| ISSN: | 1095-7219 0040-585X |
| DOI: | 10.1137/s0040585x97975939 |
| Popis: | The paper proves the central limit theorem (the logarithmic law) for random determinants under weaker conditions than the author used earlier: if for any n the random elements $\xi_{ij}^{(n)}$, $i,j=1\lz n$, of the matrix $\Xi=(\xi_{ij}/n)$ are independent, $\bE\xi_{ij}^{(n)}=a$, $\var\xi_{ij}^{(n)}=1$, and for some $\dt > 0$ $$ \sup_n\max_{i,j=1\lz n}\bE|\xn|^{4+\dt} < \iy, $$ then $$ %\eqalignno{ \lny\Big\{{\log\det\Xi^2-\log (n-1)!-\log (1+na^2)\over \sqrt{2\log n}} < x\Big\} %\cr&\q ={1\over\sqrt{2\pi}}\int_{-\iy}^x\exp\Big(-{u^2\over 2}\Big)\,du. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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