论文标题
Dyson Brownian Motion下的特征多项式产品的产物相变
Phase transitions for products of characteristic polynomials under Dyson Brownian motion
论文作者
论文摘要
我们研究了具有外部源的高斯和拉瓜勒$β$浓度的特征多项式产品的平均产品，并证明了pearcey-type相变的特定全等级源扰动。这些阶段的特征是确定特征多项式平均产物的缩放限制的显式功能形式，这些尺寸为某些多维积分，其尺寸等于产品数量。
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.
