正矩阵与张量相互作用的中间场表示
Intermediate Field Representation for Positive Matrix and Tensor Interactions
摘要：
在本文中，我们引入了一个中间域表示的随机矩阵和随机张量的正（稳定）的相互作用的程度高于4。这种表征尊重了负责积极性的对称轴。它是非微扰的，并允许证明，这些模型是Borel-Le Roy求和的适当的顺序，在其耦合常数。然而，我们还没有能够将收敛的Loop Vertex Expansion与这种表示相关联，因此当矩阵或张量的大小N趋于无穷大时，我们的Borel可和性结果不是最佳的期望形式。
英文摘要：
In this paper we introduce an intermediate field representation for random matrices and random tensors with positive (stable) interactions of degree higher than 4. This representation respects the symmetry axis responsible for positivity. It is non-perturbative and allows to prove that such models are Borel-Le Roy summable of the appropriate order in their coupling constant. However we have not been able yet to associate a convergent Loop Vertex Expansion to this representation, hence our Borel summability result is not of the optimal expected form when the size N of the matrix or of the tensor tends to infinity.
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