A dynamical version of the SYK Model and the q-Brownian Motion
Operator Algebras
2020-09-09 v3 Mathematical Physics
math.MP
Probability
Abstract
We extend recent results on the asymptotic eigenvalue distribution of the SYK model to the multivariate case and relate the limit of a dynamical version of the SYK model with the q-Brownian motion, a non-commutative deformation of classical Brownian motion. Furthermore, we extend the results for fluctuations to the multivariate setting and treat also higher correlation functions. The structure of our results for the sparse SYK random matrices resembles the formulas for higher order freeness for ordinary GUE random matrices.
Keywords
Cite
@article{arxiv.1905.12999,
title = {A dynamical version of the SYK Model and the q-Brownian Motion},
author = {Miguel Pluma and Roland Speicher},
journal= {arXiv preprint arXiv:1905.12999},
year = {2020}
}
Comments
we provide more details in some proofs to close some gaps from the previous version; a new figure is added in order to address possible relation with "higher order freeness"