Naoki Sasakura: Signed eigenvalue/vector distribution of complex random tensor


Eigenvalue/vector distributions of random tensors can be rewritten as partition functions of quantum field theories, that allows systematic, widely applicable, and powerful analysis of the distributions. In particular singed distributions can be rewritten as four-fermi theories, which are in principle always exactly computable. Though signed distributions are different from genuine distributions, they are expected to be intimately related and coincident near their endpoints, which have applications to such as geometric measure of entanglement, the largest eigenvalue, and the best rank-one approximation. In this talk, we apply the method to the signed eigenvalue/vector distribution of complex random tensor, and obtain an exact compact expression. We then compute the endpoint of the distribution in the large dimension limit and also that in the large order limit. An open question is pointed out concerning the latter.

The agenda of this meeting is empty