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.

中文翻译：

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SYK 模型和 q-布朗运动的动力学版本

我们将最近关于 SYK 模型的渐近特征值分布的结果扩展到多变量情况，并将 SYK 模型的动态版本的极限与q-布朗运动，经典布朗运动的非交换变形。此外，我们将波动的结果扩展到多变量设置，并处理更高的相关函数。我们对稀疏 SYK 随机矩阵的结果结构类似于普通 GUE 随机矩阵的高阶自由度公式。