Melonic dominance and the largest eigenvalue of a large random tensor
From MaRDI portal
Publication:6337377
DOI10.1007/S11005-021-01407-ZarXiv2003.11220MaRDI QIDQ6337377
Author name not available (Why is that?)
Publication date: 25 March 2020
Abstract: We consider a Gaussian rotationally invariant ensemble of random real totally symmetric tensors with independent normally distributed entries, and estimate the largest eigenvalue of a typical tensor in this ensemble by examining the rate of growth of a random initial vector under successive applications of a nonlinear map defined by the random tensor. In the limit of a large number of dimensions, we observe that a simple form of melonic dominance holds, and the quantity we study is effectively determined by a single Feynman diagram arising from the Gaussian average over the tensor components. This computation suggests that the largest tensor eigenvalue in our ensemble in the limit of a large number of dimensions is proportional to the square root of the number of dimensions, as it is for random real symmetric matrices.
No records found.
This page was built for publication: Melonic dominance and the largest eigenvalue of a large random tensor
Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6337377)
