Singularity dominated strong fluctuations for some random matrix averages
P. J. Forrester, J. P. Keating
Abstract
The circular and Jacobi ensembles of random matrices have their eigenvalue support on the unit circle of the complex plane and the interval (0,1) of the real line respectively. The averaged value of the modulus of the corresponding characteristic polynomial raised to the power 2 μ diverges, for 2μ -1, at points approaching the eigenvalue support. Using the theory of generalized hypergeometric functions based on Jack polynomials, the functional form of the leading asymptotic behaviour is established rigorously. In the circular ensemble case this confirms a conjecture of Berry and Keating.
Create a lesson
Related papers
Phase transitions in non-Hermitian spherical integrals
Pierre Bousseyroux, Marc Potters
Factorization method for a clamped obstacle from near-field measurements via a far-field transformation
General Ozochiawaeze, Isaac Harris
Asymmetric phase transitions in random noncommutative geometries
Benedek Bukor, Masoud Khalkhali, Samuel Kováčik et al.
A Cumulative Framework for Solid Deformation
Lev Steinberg
Classification of pairs of second-order Hamiltonian operators and hydrodynamic type systems in six components
Giorgio Gubbiotti, Lambertus Van Geemen, Pierandrea Vergallo
Reconstructability of Inverse Problems under Symmetry: Separating Structural, Effective, and Physical Upper Bounds
Isshin Arai