We consider a Gaussian rotationally invariant ensemble of random real totally symmetric tensors with independent normally distributed entries, and estimate the largest eigenvalue of a typical tensor in this ensemble by examining the rate of growth of a random initial vector under successive applications of a nonlinear map defined by the random tensor. In the limit of a large number of dimensions, we observe that a simple form of melonic dominance holds, and the quantity we study is effectively determined by a single Feynman diagram arising from the Gaussian average over the tensor components. This computation suggests that the largest tensor eigenvalue in our ensemble in the limit of a large number of dimensions is proportional to the square root of the number of dimensions, as it is for random real symmetric matrices.

我们考虑具有独立正态分布项的随机实完全对称张量的高斯旋转不变集合，并通过在定义的非线性映射的连续应用下检查随机初始向量的增长率来估计该集合中典型张量的最大特征值由随机张量。在大量维数的限制中，我们观察到，简单的旋律支配地位成立，并且我们研究的数量有效地由张量分量上的高斯平均值产生的单个费曼图确定。该计算表明，在大量维数的限制中，我们的合奏中最大的张量本征值与维数个数的平方根成正比，就像随机实对称矩阵一样。