论文标题
高斯张量模型的真实张量特征向量的签名分布通过四型富米理论
Signed distributions of real tensor eigenvectors of Gaussian tensor model via a four-fermi theory
论文作者
论文摘要
特征值分布是矩阵模型中重要的动力学数量，在张量模型中得出它们是一个具有挑战性的问题。在本文中，我们将带有高斯分布的三个张量视为最简单的情况，并获得了用于实际张量特征向量的签名分布的明确公式：每个真实的张量特征向量都会通过$ \ pm 1 $ 1 $贡献，这取决于$ \ pm 1 $。该公式由第二种汇合的超几何函数表达，该函数是通过计算四型Fermi理论的分区函数而获得的。该公式还可以用作实际特征向量分布的下限（没有迹象），并且通过与蒙特卡洛模拟进行比较来讨论它们的紧密度/松散性。限制了很大的限制，并保留了公式的特征性振荡行为。
Eigenvalue distributions are important dynamical quantities in matrix models, and it is a challenging problem to derive them in tensor models. In this paper, we consider real symmetric order-three tensors with Gaussian distributions as the simplest case, and derive an explicit formula for signed distributions of real tensor eigenvectors: Each real tensor eigenvector contributes to the distribution by $\pm 1$, depending on the sign of the determinant of an associated Hessian matrix. The formula is expressed by the confluent hypergeometric function of the second kind, which is obtained by computing a partition function of a four-fermi theory. The formula can also serve as lower bounds of real eigenvector distributions (with no signs), and their tightness/looseness are discussed by comparing with Monte Carlo simulations. Large-$N$ limits are taken with the characteristic oscillatory behavior of the formula being preserved.
