Asymptotics of the Airy-kernel determinant
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
相关论文
Airy-kernel determinant on two large intervals
We find the probability of two gaps of the form $(sc,sb)\cup (sa,+\infty)$, $c<b<a<0$, for large $s>0$, in the edge scaling limit of the Gaussian Unitary Ensemble of random matrices, including the multiplicative constant in the asymptotics.
math-phmath.FAmath.MP
Determinants of Airy Operators and Applications to Random Matrices
The purpose of this paper is to describe asymptotic formulas for determinants of certain operators that are analogues of Wiener-Hopf operators. The determinant formulas yield information about the distribution functions for certain random variables that arise in random matrix theory when one rescales at the edge of the spectrum.
math.FAnlin.SIsolv-int
Sine-kernel determinant on two large intervals
We consider the probability of two large gaps (intervals without eigenvalues) in the bulk scaling limit of the Gaussian Unitary Ensemble of random matrices. We determine the multiplicative constant in the asymptotics. We also provide the full explicit asymptotics (up to decreasing terms) for the transition between one and two large gaps.
math-phmath.FAmath.MP
Asymptotics for a determinant with a confluent hypergeometric kernel
We obtain "large gap" asymptotics for a Fredholm determinant with a confluent hypergeometric kernel. We also obtain asymptotics for determinants with two types of Bessel kernels which appeared in random matrix theory.
math-phmath.CAmath.FA
Large gap asymptotics for random matrices
We outline an approach recently used to prove formulae for the multiplicative constants in the asymptotics for the sine-kernel and Airy-kernel determinants appearing in random matrix theory and related areas.
math-phmath.CAmath.FA
Matrix balls, radial analysis of Berezin kernels, and hypergeometric determinants
Consider the pseidounitary group $G=U(p,q)$ and its compact subgroup $K=U(p)$. We construct an explicit unitary intertwining operator from the tensor product of a holomorphic representation and a antiholomorphic representation of $G$ to the space $L^2(G/K)$. This implies the existense of a canonical action of the group $G\times G$ in $L^2(G/K)$. We also give a survey of analysis of Berezin kernels and their relations with special functions.
math-phmath.CAmath.CV
更多相关论文收起更多论文
Dyson's constant in the asymptotics of the Fredholm determinant of the sine kernel
We prove that the asymptotics of the Fredholm determinant of $I-K_α$, where $K_α$ is the integral operator with the sine kernel $\sin(x-y)/(x-y)/π$ on the interval $[0,α]$ is given by a formula which was conjectured by F.J. Dyson. The first and second order asymptotics as well as the higher order asymptotics except for the constant term have already been proved. In this paper we thus determine the constant term.
math.FA
Dyson's constants in the asymptotics of the determinants of Wiener-Hopf-Hankel operators with the sine kernel
In this paper we are going to prove two asymptotic formulas for determinants det(I-K_s), as s goes to infinity, where K_s are the Wiener-Hopf-Hankel operators acting on L^2[0,s] with the kernels K(x-y)+K(x+y) and K(x-y)-K(x+y), respectively, and K(t):=sin(t)/(π*t). These formulas were conjectured by Dyson. The identification of the constant term in the asymptotics was an open problem for a long time.
math.FA
The asymptotics a Bessel-kernel determinant which arises in Random Matrix Theory
In Random Matrix Theory the local correlations of the Laguerre and Jacobi Unitary Ensemble in the hard edge scaling limit can be described in terms of the Bessel kernel (containing a parameter $α$). In particular, the so-called hard edge gap probabilities can be expressed as the Fredholm determinants of the corresponding integral operator restricted to the finite interval [0, R]. Using operator theoretic methods we are going to compute their asymptotics as R goes to infinity under certain assumption on the parameter $α$.
math.CAmath.FA
实线上矩阵值核的数值Fredholm行列式
Numerical Fredholm determinants for matrix-valued kernels on the real line
本研究拓展了Bornemann的分析，提出一种计算实线上矩阵值核定义的迹类、希尔伯特-施密特积分算子Fredholm行列式的数值方法，推导了截断与求积误差估计，并在Birman-Schwinger算子上验证了效果。
cs.NAmath.FAmath.NA
Heat Kernel Asymptotics, Path Integrals and Infinite-Dimensional Determinants
We investigate the short-time expansion of the heat kernel of a Laplace type operator on a compact Riemannian manifold and show that the lowest order term of this expansion is given by the Fredholm determinant of the Hessian of the energy functional on a space of finite energy paths. This is the asymptotic behavior to be expected from formally expressing the heat kernel as a path integral and then (again formally) using Laplace's method on the integral. We also relate this to the zeta determinant of the Jacobi operator, which is another way to assign a determinant to the Hessian of the energy …
math.APmath.DGmath.FA
On the extension of Fredholm determinants to the mixed multidimensional integral operators with regulated kernels
We extend the classical trace (and determinant) known for the integral operators $$ ({\mathcal I}+)\int_{[0,1)^N}{\bf A}({\bf k},{\bf x}){\bf u}({\bf x})d{\bf x} $$ with matrix-valued kernels ${\bf A}$ to the operators of the form $$ \sum_α\int_{[0,1)^{|α|}}{\bf A}({\bf k},{\bf x}_α){\bf u}({\bf k}_{\overlineα},{\bf x}_α)d{\bf x}_α, $$ where $α$ are arbitrary subsets of the set $\{1,...,N\}$. Such operators form a Banach algebra containing simultaneously all integral operators of the dimensions $\leqslant N$. In this sense, it is a largest algebra where explicit traces and determinants are con…
math.FA
具有贝塞尔核的行列式点过程的中心极限定理收敛速度
Speed of convergence in the Central Limit Theorem for the determinantal point process with the Bessel kernel
本文研究由汉克尔变换对角化的线性算子的弗雷德霍姆行列式渐近展开，推导出渐近小因子的显式公式，并将其应用于贝塞尔核行列式点过程，计算了加性泛函在柯尔莫哥洛夫-斯米尔诺夫度量下的中心极限定理收敛速度。
math.FAmath.PR
