Related papers: Signed eigenvalue/vector distribution of complex o…
Quantum field theories can be applied to compute various statistical properties of random tensors. In particular signed distributions of tensor eigenvalues/vectors are the easiest, which can be computed as partition functions of four-fermi…
Eigenvalue distributions are important dynamical quantities in matrix models, and it is a challenging problem to derive them in tensor models. In this paper, we consider real symmetric order-three tensors with Gaussian distributions as the…
Random tensor models have applications in a variety of fields, such as quantum gravity, quantum information theory, mathematics of modern technologies, etc., and studying their statistical properties, e.g., tensor eigenvalue/vector…
Eigenvalue distributions are important dynamical quantities in matrix models, and it is an interesting challenge to study corresponding quantities in tensor models. We study real tensor eigenvalue/vector distributions for real symmetric…
Real eigenpairs of a real antisymmetric tensor of order $p$ and dimension $N$ can be defined as pairs of a real eigenvalue and $p$ orthonormal $N$-dimensional real eigenvectors. We compute the signed and the genuine distributions of such…
The largest eigenvalue of random tensors is an important feature of systems involving disorder, equivalent to the ground state energy of glassy systems or to the injective norm of quantum states. For symmetric Gaussian random tensors of…
As in random matrix theories, eigenvector/value distributions are important quantities of random tensors in their applications. Recently, real eigenvector/value distributions of Gaussian random tensors have been explicitly computed by…
We obtain exact analytic expressions of real tensor eigenvalue/vector distributions of real symmetric order-three tensors with Gaussian distributions for $N\leq 8$. This is achieved by explicitly computing the partition function of a…
We compute the joint distributions of arbitrary numbers of eigenvectors of real and complex symmetric random tensors by the quantum field theoretical methods which were previously used to compute the mean distributions. We obtain the random…
We present some new results on the joint distribution of an arbitrary subset of the ordered eigenvalues of complex Wishart, double Wishart, and Gaussian hermitian random matrices of finite dimensions, using a tensor pseudo-determinant…
We investigate the distribution of eigenvalues of weighted adjacency matrices from a specific ensemble of random graphs. We distribute $N$ vertices across a fixed number $\kappa$ of components, with asymptotically $\alpha_j \dot N$ vertices…
Eigenvectors of tensors, as studied recently in numerical multilinear algebra, correspond to fixed points of self-maps of a projective space. We determine the number of eigenvectors and eigenvalues of a generic tensor, and we show that the…
Irregularities in the metric tensor of a signature-changing space-time suggest that field equations on such space-times might be regarded as distributional. We review the formalism of tensor distributions on differentiable manifolds, and…
Tensor-valued and matrix-valued measurements of different physical properties are increasingly available in material sciences and medical imaging applications. The eigenvalues and eigenvectors of such multivariate data provide novel and…
In this paper we focus on the large n probability distribution function of the largest eigenvalue in the Gaussian Orthogonal Ensemble of n by n matrices (GOEn). We prove an Edgeworth type Theorem for the largest eigenvalue probability…
Eigenvector centrality is one of the outstanding measures of central tendency in graph theory. In this paper we consider the problem of calculating eigenvector centrality of graph partitioned into components and how this partitioning can be…
The limiting distribution of eigenvalues of N x N random matrices has many applications. One of the most studied ensembles are real symmetric matrices with independent entries iidrv; the limiting rescaled spectral measure (LRSM)…
Given two positive integers $n$ and $k$ and a parameter $t\in (0,1)$, we choose at random a vector subspace $V_{n}\subset \mathbb{C}^{k}\otimes\mathbb{C}^{n}$ of dimension $N\sim tnk$. We show that the set of $k$-tuples of singular values…
Observables in random tensor theory are polynomials in the entries of a tensor of rank $d$ which are invariant under $U(N)^d$. It is notoriously difficult to evaluate the expectations of such polynomials, even in the Gaussian distribution.…
We derive efficient recursive formulas giving the exact distribution of the largest eigenvalue for finite dimensional real Wishart matrices and for the Gaussian Orthogonal Ensemble (GOE). In comparing the exact distribution with the…