@unpublished{B-The-Average-Number-Of-Critical-Rank-One-Approximations-To-A-Symmetric-Tensor,
Title = {The average number of critical rank-one-approximations to a symmetric tensor},
Author = {Paul Breiding},
Year = {2017},
Month = {1},
Abstract = {Given a real symmetric tensor $v\in(\Bbb R^n)^{\otimes p}$ of order $p$, a critical rank-one approximation of $v$ is a local minimum of the euclidean distance from the set of symmetric rank-1 tensors to $v$. We compute the expected number of critical rank-one-approximations to a random tensor drawn from the standard Gaussian distribution relative to the Bombieri norm. This answers a question posed by Draisma and Horobet, who asked for a closed formula of this expectation. The computation requires to compute the expected absolute value of the determinant of a matrix from the Gaussian Orthogonal Ensemble.},
Url = {http://arxiv.org/abs/1701.07312}
}