Würfel, Tim Robert: Characteristic polynomials of random matrices and their role in an effective theory of strong interactions. 2021
Inhalt
- Introduction
- Mathematical and Physical Framework
- Random matrix models for QCD
- Joint Probability Density Function
- Orthogonal Polynomials
- Scaling Limits and universality
- Determinantal Point Processes
- Expectation Values of Characteristic Polynomials in Polynomial Ensembles
- Determinantal structures in polynomial ensembles
- Results for Invertible Polynomial Ensembles
- Reweighting of expectation values
- Summary
- Asymptotic Analysis of Correlation Kernels
- Universality
- Equivalence with results for zero temperature models
- Equivalence with results obtained via SUSY techniques
- Summary
- Concluding Remarks and Outlook
- Properties of Vandermonde Determinants
- Determinantal Formulae for Characteristic Polynomials
- Derivation of Joint Probability Density Functions
- Polynomial Ensembles as Giambelli compatible Point Processes
- Bibliography