Add to ORKGWe 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 higher-order analogues of the Airy kernel and are built out of functions associated with the Painleve I hierarchy. The Fredholm determinants related to those kernels are higher-order generalizations of the Tracy-Widom distribution. We give an explicit expression for the determinants in terms of a distinguished smooth solution to the Painleve II hierarchy. In addition, we compute large gap asymptotics for the Fredholm determinants. (c) 2009 Wiley Periodicals, Inc
In random matrix theory, the Tracy-Widom (TW) distribution describes the behavior of the largest eig...
Orthogonal polynomial random matrix models of NxN hermitian matrices lead to Fredholm determinants o...
We compute asymptotics for Hankel determinants and orthogonal polynomials with respect to a disconti...
We study a family of distributions that arise in critical unitary random matrix ensembles. They are ...
Akemann G, Atkin M. Higher Order Analogues of Tracy-Widom Distributions via the Lax Method. J.Phys. ...
We study a family of distributions that arise in critical unitary random matrix ensembles. They are ...
We study Fredholm determinants of a class of integral operators, whose kernels can be expressed as d...
33 pages, 5 figuresWe study Fredholm determinants of a class of integral operators, whose kernels ca...
The Painlevé II hierarchy is a sequence of nonlinear ODEs, with the Painlevé II equation as first me...
For a wide class of Hermitian random matrices, the limit distribution of the eigenvalues close to th...
We study the distribution of the smallest eigenvalue for certain classes of positive-definite Hermit...
Scaling level-spacing distribution functions in the ``bulk of the spectrum'' in random matr...
We obtain large gap asymptotics for Airy kernel Fredholm determinants with any number m of discontin...
We study unitary invariant random matrix ensembles with singular potentials. We obtain asymptotics f...
We describe a new universality class for unitary invariant random matrix ensembles. It arises in the...
In random matrix theory, the Tracy-Widom (TW) distribution describes the behavior of the largest eig...
Orthogonal polynomial random matrix models of NxN hermitian matrices lead to Fredholm determinants o...
We compute asymptotics for Hankel determinants and orthogonal polynomials with respect to a disconti...
We study a family of distributions that arise in critical unitary random matrix ensembles. They are ...
Akemann G, Atkin M. Higher Order Analogues of Tracy-Widom Distributions via the Lax Method. J.Phys. ...
We study a family of distributions that arise in critical unitary random matrix ensembles. They are ...
We study Fredholm determinants of a class of integral operators, whose kernels can be expressed as d...
33 pages, 5 figuresWe study Fredholm determinants of a class of integral operators, whose kernels ca...
The Painlevé II hierarchy is a sequence of nonlinear ODEs, with the Painlevé II equation as first me...
For a wide class of Hermitian random matrices, the limit distribution of the eigenvalues close to th...
We study the distribution of the smallest eigenvalue for certain classes of positive-definite Hermit...
Scaling level-spacing distribution functions in the ``bulk of the spectrum'' in random matr...
We obtain large gap asymptotics for Airy kernel Fredholm determinants with any number m of discontin...
We study unitary invariant random matrix ensembles with singular potentials. We obtain asymptotics f...
We describe a new universality class for unitary invariant random matrix ensembles. It arises in the...
In random matrix theory, the Tracy-Widom (TW) distribution describes the behavior of the largest eig...
Orthogonal polynomial random matrix models of NxN hermitian matrices lead to Fredholm determinants o...
We compute asymptotics for Hankel determinants and orthogonal polynomials with respect to a disconti...