The expected number of Z-eigenvalues of a real gaussian tensor

2016/04/13 by Breiding, Paul
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1604.03910

Abstract

A real number λ is called a Z-eigenvalue of a tensor A, if λ is an eigenvalue of A and the corresponding eigenvector v is real and satisfies v^Tv=1. In this paper we compute the expected number of Z-eigenvalues of a real gaussian tensor and its asymptotic behaviour. Here we call a tensor A=(A_i₀,…,i_d) ∈ℝ^n^d+1 gaussian, when the A_i₀,…,i_d are centered gaussian random variables with variance σ²= 1.

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