## Expected absolute random determinants and zonoids.(English)Zbl 0739.15015

This paper is about random matrices. It studies expectations of absolute values of determinants of random matrices which have as columns i.i.d. copies of a random vector. The results relates these to the volume of zonoids which are limits of zonotopes in the Hausdorff metric (a zonotope is a finite sum of line segments). Also some bounds are given.

### MSC:

 15B52 Random matrices (algebraic aspects) 52A40 Inequalities and extremum problems involving convexity in convex geometry 60D05 Geometric probability and stochastic geometry 60E15 Inequalities; stochastic orderings 15A42 Inequalities involving eigenvalues and eigenvectors 52A22 Random convex sets and integral geometry (aspects of convex geometry)

### Keywords:

random matrices; determinants; zonoids; zonotopes
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