置换不变高斯2-矩阵模型
Permutation invariant Gaussian 2-matrix models
摘要：
我们构造了任意大小矩阵的一般置换不变高斯2-矩阵模型$D$。该模型的参数是使用对称群$S_D$的表示理论定义的变量。建立了矩阵变量（模型的观测量）的置换不变多项式函数与有向着色图之间的对应关系，从而揭示了这些不变量的大$D$计数的稳定性。图的精细计数是根据涉及置换群的双陪集给出的，置换群由图的局部结构定义。线性和二次观测量被转换为一个$S_D$表示理论基础，并用于定义收敛的高斯测度。根据表示论参数给出了计算任意次图基观测量期望值的微扰规则。一些可观的程度高达四个明确的结果给出了随着一个圣人程序，计算一般的期望值。
英文摘要：
We construct the general permutation invariant Gaussian 2-matrix model for matrices of arbitrary size $D$. The parameters of the model are given in terms of variables defined using the representation theory of the symmetric group $S_D$. A correspondence is established between the permutation invariant polynomial functions of the matrix variables (the observables of the model) and directed colored graphs, which sheds light on stability properties in the large $D$ counting of these invariants. The refined counting of the graphs is given in terms of double cosets involving permutation groups defined by the local structure of the graphs. Linear and quadratic observables are transformed to an $S_D$ representation theoretic basis and are used to define the convergent Gaussian measure. The perturbative rules for the computation of expectation values of graph-basis observables of any degree are given in terms of the representation theoretic parameters. Explicit results for a number of observables of degree up to four are given along with a Sage programme that computes general expectation values.
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