We study the averaged products of characteristic polynomials for the Gaussian and Laguerre β-ensembles with external source, and prove Pearcey-type phase transitions for particular full rank perturbations of source. The phases are characterised by determining the explicit functional forms of the scaled limits of the averaged products of characteristic polynomials, which are given as certain multidimensional integrals, with dimension equal to the number of products.

中文翻译：

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戴森布朗运动下特征多项式乘积的相变

我们研究了具有外部源的高斯和拉盖尔 β 系综的特征多项式的平均乘积，并证明了特定全秩扰动的 Pearcey 型相变。这些阶段的特征在于确定特征多项式的平均乘积的标度极限的显式函数形式，这些多项式作为某些多维积分给出，维数等于乘积的数量。