Signed distributions of real tensor eigenvectors of Gaussian tensor model via a four-fermi theory

Eigenvalue distributions are important dynamical quantities in matrix models, and it is a challenging problem to derive them tensor models. In this paper, we consider real symmetric order-three tensors with Gaussian as the simplest case, an explicit formula for signed of eigenvectors: Each eigenvector contributes distribution by ±1, depending on sign determinant associated Hessian matrix. The expressed confluent hypergeometric function second kind, which obtained computing partition four-fermi theory. can also serve lower bounds (with no signs), their tightness/looseness discussed comparing Monte Carlo simulations. Large-N limits taken characteristic oscillatory behavior being preserved.