We construct approximate transport maps for perturbative several-matrix models. As a consequence, we deduce that local statistics have the same asymptotic as in the case of independent GUE or GOE matrices (i.e., they are given by the sine-kernel in the bulk and the Tracy–Widom distribution at the edge), and we show averaged energy universality (i.e., universality for averages of m-points correlation functions around some energy level E in the bulk). As a corollary, these results yield universality for self-adjoint polynomials in several independent GUE or GOE matrices which are close to the identity.

中文翻译：

---

通过近似传输图在多矩阵模型中的普遍性

我们为微扰多矩阵模型构建近似传输图。因此，我们推导出局部统计量与独立 GUE 或 GOE 矩阵的情况具有相同的渐近性（即，它们由块中的正弦核和边缘处的 Tracy-Widom 分布给出），并且我们显示平均能量普遍性（即，在体中某个能级 E 周围 m 点相关函数的平均值的普遍性）。作为推论，这些结果对接近恒等式的几个独立 GUE 或 GOE 矩阵中的自伴随多项式产生了普遍性。