Double scaling limits of Toeplitz, Hankel and Fredholm determinants
(2017)
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- Authors
- Supervisors
- Claeys, Tom
- Abstract
- Toeplitz, Hankel and Fredholm determinants occur naturally in the study of the eigenvalues of the Circular Unitary Ensemble and the Gaussian Unitary Ensemble (GUE) of random matrices, as partition functions and gap probabilities. The thesis has two main parts. First, we consider the asymptotic probability of having two large gaps in the distribution of eigenvalues in the bulk scaling limit of random matrices, which is given by the Fredholm determinant of the sine kernel on two large intervals. The approach we take is through the study of Toeplitz determinants and orthogonal polynomials on the unit circle. This is based on joint work with Igor Krasovsky. Secondly, we consider statistics of the characteristic polynomials of the GUE. We view these statistics as a Hankel determinant, for which we study the asymptotics. This is based on joint work with Tom Claeys.
- Affiliations
Citations
Fahs, B. (2017). Double scaling limits of Toeplitz, Hankel and Fredholm determinants. https://hdl.handle.net/2078.5/65670