Matrix integrals and Hurwitz numbers
Matrix integrals and Hurwitz numbers
复制标题
矩阵积分和赫维茨数
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
A. Orlov
中科院分区：
文献类型：
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作者：
A. Orlov
我们研究的多矩阵模型可以看作是依赖于随机矩阵积的特征值的函数积的积分。在本文中，我们考虑了两分量KP（半无限相对论Toda格）层次和Kac和van de Leur引入的BKP层次的tau函数。有时这样的积分本身就是函数。我们考虑产生赫尔维茨数$H^{e},f$的模型，其中$e$是基面的欧拉特征，$f$是分支点的数目。我们表明,以防被积函数包含n > 2美元矩阵的乘积的积分产生避署2美元的赫维茨数字,通过n + 2美元,两个数字e和f依赖美元美元对美元$ n和矩阵乘积因子的顺序。欧拉特征$ e $可以是偶数或奇数，即匹配可定向和不可定向（Klein）基面，这取决于被积函数中BKP层次的tau函数的存在。我们研究了两种情况：复矩阵的乘积和酉矩阵的乘积。
We study multi-matrix models which may be viewed as integrals of products of tau functions which depend on the eigenvalues of products of random matrices. In the present paper we consider tau functions of the hierarchy the two-component KP (semiinfinite relativistic Toda lattice) and of hierarchy of the BKP introduced by Kac and van de Leur. Sometimes such integrals are tau functions themselves. We consider models which generate Hurwitz numbers $H^{e},f$, where $e$ is the Euler characteristic of the base surface and $f$ is the number of branch points. We show that in case the integrands contains the product of $n > 2$ matrices the integral generates Hurwitz numbers with $ele 2$ and $fle n+2$, both numbers $e$ and $f$ depend both on $n$ and on the order of the multipliers in the matrix product. The Euler characteristic $ e $ can be either an even or an odd number, that is, match both orientable and nonorientable (Klein) base surfaces, depending on the presence of the tau function of the BKP hierarchy in the integrand. We study two cases: the products of complex and the products of unitary matrices.
影响因子：
2.4
作者：
Akemann, Gernot;Ipsen, Jesper R.;Kieburg, Mario
通讯作者：
Kieburg, Mario
影响因子：
1.7
作者：
Akemann, Gernot;Strahov, Eugene
通讯作者：
Strahov, Eugene