论文标题
关于随机矩阵的产品
On Products of Random Matrices
论文作者
论文摘要
我们介绍了一个模型家族，我们将其命名为与儿童图纸相关的矩阵模型 - 所谓的Dessin d'Enfant。 dessins d'enfant是在可封闭的可定向表面（在天空中）上绘制的特殊类型的图。这样的图的顶点是我们称为星星的小磁盘。我们将随机矩阵附加到图形的边缘，并获取多层次模型。此外，在恒星上，我们附着源矩阵。他们发挥自由参数或模型耦合常数的作用。我们的积分的答案是通过我们称为“恒星光谱”的数量来表达的。答案还可能包括一些组合数字，例如Hurwitz数字或小组表示理论中的字符。
We introduce a family of models, which we name matrix models associated with children's drawings -- the so-called dessin d'enfant. Dessins d'enfant are graphs of a special kind drawn on a closed connected orientable surface (in the sky). The vertices of such a graph are small disks that we call stars. We attach random matrices to the edges of the graph and get multimatrix models. Additionally, to the stars we attach source matrices. They play the role of free parameters or model coupling constants. The answers for our integrals are expressed through quantities that we call the "spectrum of stars." The answers may also include some combinatorial numbers, such as Hurwitz numbers or characters from group representation theory.
