Eigenvalue distributions play important roles in understanding the dynamics of matrix models. Then it would be a natural question what roles tensor eigenvalue/vector distributions play in tensor models. We consider here the most basic case of Gaussian tensor models, and compute the eigenvalue/vector distributions. In fact essentially the same problem has already been solved by matrix model techniques in the context of the p-spin spherical model for spin glasses. But in this talk I use more familiar field theoretical methods. A picked-up result is that, in the large-N limit, the eigenvalue distribution is Gaussian, which can be contrasted with Wigner’s semicircle law of the matrix model.
Sylvain Carrozza, Luca Lionni, Fabien Vignes-Tourneret
