Moments of random determinants

I. G. Zhurbenko

Teoriâ veroâtnostej i ee primeneniâ, Tome 13 (1968) no. 4, pp. 720-725

Résumé

Let $\Delta_n$ be a determinant with random elements $\xi_{ij}$, $i=1,\dots,n$, $j=1,,\dots,n$. In the paper the expectation $\mathbf E(\Delta_n)^2$ is calculated in case when all $\xi_{ij}$'s are independent and equally distributed. In case when $\xi_{ij}$'s are independent and equally distributed for $i\le j$, $i=1,\dots,n$, $j=1,\dots,n$, and $\xi_{ij}=\xi_{ji}$ we calculate $\mathbf E(\Delta_n)^2$ and $\mathbf E(\Delta_n)$ if $\mathbf E\xi_{ij}=0$ and $\mathbf E(\Delta_n)$ if $\mathbf(\xi_{ij})\ne0$.