# Large Gap Asymptotics for Random Matrices

@article{Krasovsky2010LargeGA, title={Large Gap Asymptotics for Random Matrices}, author={I. V. Krasovsky}, journal={arXiv: Mathematical Physics}, year={2010}, pages={413-419} }

Asymptotic behavior is discussed of the sine-kernel and Airy-kernel Fredholm determinants related to random matrices.

## 15 Citations

### Oscillatory Asymptotics for the Airy Kernel Determinant on Two Intervals

- Mathematics
- 2019

We obtain asymptotics for the Airy kernel Fredholm determinant on two intervals. We give explicit formulas for all the terms up to and including the oscillations of order $1$, which are expressed in…

### Asymptotics of the hard edge Pearcey determinant

- Mathematics
- 2022

We study the Fredholm determinant of an integral operator associated to the hard edge Pearcey kernel. This determinant appears in a variety of random matrix and non-intersecting paths models. By…

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

- Mathematics
- 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…

### Large Gap Asymptotics for Airy Kernel Determinants with Discontinuities

- MathematicsCommunications in Mathematical Physics
- 2019

We obtain large gap asymptotics for Airy kernel Fredholm determinants with any number m of discontinuities. These m-point determinants are generating functions for the Airy point process and encode…

### Large Gap Asymptotics for Airy Kernel Determinants with Discontinuities

- MathematicsCommunications in Mathematical Physics
- 2019

We obtain large gap asymptotics for Airy kernel Fredholm determinants with any number m of discontinuities. These m -point determinants are generating functions for the Airy point process and encode…

### Aspects of Toeplitz Determinants

- Mathematics
- 2011

We review the asymptotic behavior of a class of Toeplitz (as well as related Hankel and Toeplitz + Hankel) determinants which arise in integrable models and other contexts. We discuss Szego,…

### Fredholm Determinant Solutions of the Painlevé II Hierarchy and Gap Probabilities of Determinantal Point Processes

- MathematicsInternational Mathematics Research Notices
- 2019

We study Fredholm determinants of a class of integral operators, whose kernels can be expressed as double contour integrals of a special type. Such Fredholm determinants appear in various random…

### Gap Probability for the Hard Edge Pearcey Process

- MathematicsAnnales Henri Poincaré
- 2023

The hard edge Pearcey process is universal in random matrix theory and many other stochastic models. This paper deals with the gap probability for the thinned/unthinned hard edge Pearcey process over…

### Large gap asymptotics on annuli in the random normal matrix model

- Mathematics, Computer Science
- 2021

It is proved that the probability that no points lie on any number of annuli centered at 0 satisfies large n asymptotics of the form exp, where n is the number of points of the process.

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The authors use Riemann-Hilbert methods to compute the constant that arises in the asymptotic behavior of the Airy-kernel determinant of random matrix theory.

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AbstractWe prove that the asymptotics of the Fredholm determinant of I−Kα, where Kα is the integral operator with the sine kernel on the interval [0, α], are given by
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It is known that the probability Eβ(0, S) that an arbitrary interval of length S contains none of the eigenvalues of a random matrix chosen from the orthogonal (β = 1), unitary (β = 2) or symplectic…

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We consider the double-scaling limit in the hermitian matrix model for N 2D quantum gravity associated with the measure exp £ tjZ\ N^3. We show 7 = 1 that after the appropriate modification of the…

### Asymptotics of Tracy-Widom Distributions and the Total Integral of a Painlevé II Function

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The Tracy-Widom distribution functions involve integrals of a Painlevé II function starting from positive infinity. In this paper, we express the Tracy-Widom distribution functions in terms of…