Related papers: The generating function for the Airy point process…
We study Fredholm determinants related to a family of kernels which 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…
We study Fredholm determinants of the Painlev\'e II and Painlev\'e XXXIV kernels. In certain critical unitary random matrix ensembles, these determinants describe special gap probabilities of eigenvalues. We obtain Tracy-Widom formulas for…
Scaling level-spacing distribution functions in the ``bulk of the spectrum'' in random matrix models of $N\times N$ hermitian matrices and then going to the limit $N\to\infty$, leads to the Fredholm determinant of the sine kernel…
Scaling level-spacing distribution functions in the ``bulk of the spectrum'' in random matrix models of $N\times N$ hermitian matrices and then going to the limit $N\to\infty$, leads to the Fredholm determinant of the sine kernel…
We express the gap probabilities of the tacnode process as the ratio of two Fredholm determinants; the denominator is the standard Tracy-Widom distribution, while the numerator is the Fredholm determinant of a very explicit kernel…
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 distributions can be expressed as Fredholm…
Airy and Pearcey-like kernels and generalizations arising in random matrix theory are expressed as double integrals of ratios of exponentials, possibly multiplied with a rational function. In this work it is shown that such kernels are…
We study a family of distributions that arise in critical unitary random matrix ensembles. They are expressed as Fredholm determinants and describe the limiting distribution of the largest eigenvalue when the dimension of the random…
The J\'{a}nossy density for a determinantal point process is the probability density that an interval $I$ contains exactly $p$ points except for those at $k$ designated loci. The J\'{a}nossy density associated with an integrable kernel…
We undertake an analysis of Fredholm determinants arising from kernels whose defining functions satisfy a Schr\"odinger type equation. When this defining function is the Airy one, the evaluation of the corresponding Fredholm determinant…
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 probabilistic information about…
We study the one-parameter family of Fredholm determinants $\det(I-\rho^2\mathcal{K}_{n,x})$, $\rho\in\mathbb{R}$, where $\mathcal{K}_{n,x}$ stands for the integral operator acting on $L^2(x,+\infty)$ with the higher order Airy kernel. This…
We study the determinant $\det(I-K_{\textnormal{PII}})$ of an integrable Fredholm operator $K_{\textnormal{PII}}$ acting on the interval $(-s,s)$ whose kernel is constructed out of the $\Psi$-function associated with the Hastings-McLeod…
We study the distribution of the largest eigenvalue in formal Hermitian one-matrix models at multicriticality, where the spectral density acquires an extra number of k-1 zeros at the edge. The distributions are directly expressed through…
Our previous work on the one-dimensional KPZ equation with sharp wedge initial data is extended to the case of the joint height statistics at n spatial points for some common fixed time. Assuming a particular factorization, we compute an…
The distributions of the $k$-th largest level at the soft edge scaling limit of Gaussian ensembles are some of the most important distributions in random matrix theory, and their numerical evaluation is a subject of great practical…
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 matrix and statistical physics models. We…
In this paper, we are concerned with higher-order analogues of the Tracy-Widom distribution, which describe the eigenvalue distributions in unitary random matrix models near critical edge points. The associated kernels are constructed by…
The parabolic Airy process is the Airy$_2$ process minus a parabola, initially defined by its finite-dimensional distributions, which are given by a Fredholm determinant formula with the extended Airy kernel. This process is also the…
The Pearcey kernel is a classical and universal kernel arising from random matrix theory, which describes the local statistics of eigenvalues when the limiting mean eigenvalue density exhibits a cusp-like singularity. It appears in a…