Phase Transitions for Products of Characteristic Polynomials under Dyson Brownian Motion

2020/11/04 by Peter J. Forrester, Dang-Zheng Liu
Mathematics · Physics and Astronomy · #Brownian motion #Combinatorics #Dimension (graph theory) #Gaussian #Geometry and complex manifolds #Laguerre polynomials #Mathematical analysis #Mathematics #Orthogonal polynomials #Physics #Pure mathematics #Quantum mechanics #Random Matrices and Applications #Rank (graph theory) #Statistics #Stochastic processes and statistical mechanics #Type (biology) #math-ph #math.MP #math.PR #msc:15B52

paper · pdf · doi:10.1007/s10114-020-9445-7

published as Acta Mathematica Sinica, English Series 2020

openalex publication_date 2020/11/04 · openalex created_date 2020/11/23 · arxiv created 2020/12/26 · arxiv updated 2020/12/29 · openalex updated_date 2026/08/05

Abstract

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.

Citations

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