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. ...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.展开更多
基金Supported by Australian Research Council(Grant No.DP170102028)the National Natural Science Foundation of China(Grant No.11771417)the Youth Innovation Promotion Association CAS(Grant No.2017491)。
文摘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.
