  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.
