Random determinants, mixed volumes of ellipsoids, and zeros of Gaussian random fields

Zakhar Kabluchko, Dmitry Zaporozhets

Consider a $d\times d$ matrix $M$ whose rows are independent centered non-degenerate Gaussian vectors ${\xi }_1,...,{\xi }_d$ with covariance matrices ${\Sigma }_1,...,{\Sigma }_d$. Denote by $\mathcal{E}_i…