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Joint distributions of eigenvectors of symmetric random tensors
Naoki Sasakura
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…
Real eigenvalue/vector distributions of random real antisymmetric tensors
Nicolas Delporte, Giacomo La Scala, Naoki Sasakura +1
Real eigenpairs of a real antisymmetric tensor of order and dimension can be defined as pairs of a real eigenvalue and orthonormal -dimensional real eigenvectors. We…
Renormalization group-like flows in randomly connected tensor networks
Naoki Sasakura
Randomly connected tensor networks (RCTN) are the dynamical systems defined by summing over all the possible networks of tensors. Because of the absence of fixed lattice structure,…
Three cases of complex eigenvalue/vector distributions of symmetric order-three random tensors
Swastik Majumder, Naoki Sasakura
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 sta…
The Edge of Random Tensor Eigenvalues with Deviation
Nicolas Delporte, Naoki Sasakura
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…
Signed eigenvalue/vector distribution of complex order-three random tensor
Naoki Sasakura
We compute the signed distribution of the eigenvalues/vectors of the complex order-three random tensor by computing a partition function of a four-fermi theory, where signs are fro…
Usefulness of signed eigenvalue/vector distributions of random tensors
Max Regalado Kloos, Naoki Sasakura
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,…
Real eigenvector distributions of random tensors with backgrounds and random deviations
Naoki Sasakura
As in random matrix theories, eigenvector/value distributions are important quantities of random tensors in their applications. Recently, real eigenvector/value distributions of Ga…