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Toeplitz determinants with merging singularities

- T. Claeys, I. Krasovsky
- Mathematics
- 14 March 2014

We study asymptotic behavior for determinants of n×n Toeplitz matrices corresponding to symbols with two Fisher-Hartwig singularities at the distance 2t≥0 from each other on the unit circle. We… Expand

Biorthogonal ensembles with two-particle interactions

- T. Claeys, Stefano Romano
- Mathematics
- 10 December 2013

We investigate determinantal point processes on [0, +∞) of the form We prove that the biorthogonal polynomials associated with such models satisfy a recurrence relation and a Christoffel–Darboux… Expand

Multi-critical unitary random matrix ensembles and the general Painlevé II equation

- T. Claeys, A. Kuijlaars, M. Vanlessen
- Mathematics
- 31 August 2005

We study unitary random matrix ensembles of the form Z-'N\detM\2«e-NTrVWdM, where a > -1/2 and V is such that the limiting mean eigenvalue density for n, N - > oc and n/N - ► 1 vanishes quadratically… Expand

Hankel Determinant and Orthogonal Polynomials for a Gaussian Weight with a Discontinuity at the Edge

- A. Bogatskiy, T. Claeys, A. Its
- Mathematics
- 7 July 2015

We compute asymptotics for Hankel determinants and orthogonal polynomials with respect to a discontinuous Gaussian weight, in a critical regime where the discontinuity is close to the edge of the… Expand

Higher‐order analogues of the Tracy‐Widom distribution and the Painlevé II hierarchy

- T. Claeys, I. Krasovsky, A. Its
- Mathematics
- 16 January 2009

We study Fredholm determinants related to a family of kernels that describe the edge eigenvalue behavior in unitary random matrix models with critical edge points. The kernels are natural… Expand

Universality of the double scaling limit in random matrix models

- T. Claeys, A. Kuijlaars
- Mathematics
- 31 January 2005

We study unitary random matrix ensembles in the critical case where the limiting mean eigenvalue density vanishes quadratically at an interior point of the support. We establish universality of the… Expand

Large Gap Asymptotics at the Hard Edge for Product Random Matrices and Muttalib–Borodin Ensembles

- T. Claeys, M. Girotti, Dries Stivigny
- Mathematics
- 6 December 2016

We study the distribution of the smallest eigenvalue for certain classes of positive-definite Hermitian random matrices, in the limit where the size of the matrices becomes large. Their limit… Expand

Random Matrices with Equispaced External Source

We study Hermitian random matrix models with an external source matrix which has equispaced eigenvalues, and with an external field such that the limiting mean density of eigenvalues is supported on… Expand

Random Matrix Ensembles with Singularities and a Hierarchy of Painlevé III Equations

- Max R. Atkin, T. Claeys, F. Mezzadri
- Mathematics
- 19 January 2015

We study unitary invariant random matrix ensembles with singular potentials. We obtain asymptotics for the partition functions associated to the Laguerre and Gaussian Unitary Ensembles perturbed with… Expand

Random matrices with merging singularities and the Painlevé V equation

- T. Claeys, Benjamin Fahs
- Mathematics
- 27 August 2015

We study the asymptotic behavior of the partition function and the correlation kernel in random matrix ensembles of the form 1 Zn det M 2 tI e nTrV (M) dM, where M is an n n Hermitian matrix, > 1=2… Expand

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