Related papers: Asymptotics of the hard edge Pearcey determinant

As Fredholm determinants are more and more frequent in the context of stochastic integrability, we unveil the existence of a common framework in many integrable systems where they appear. This consists in a quasi-universal hierarchy of…

We consider a number of combinatorial problems in which rational generating functions may be obtained, whose denominators have factors with certain singularities. Specifically, there exist points near which one of the factors is asymptotic…

It is shown how to calculate asymptotics of integrals over the positive semi-axis of two functions related to the Degenerate Third Painlev\'e Equation (dP3). As an example, the corresponding results for the meromorphic solution of the dP3…

Explicit representations of the eigenvalues of the peridynamic operator have been recently derived in [5]. These representations are given in terms of generalized hypergeometric functions. Asymptotic analysis of the hypergeometric functions…

We obtain an identity between Fredholm determinants of two kinds of operators, one acting on functions on the unit circle and the other acting on functions on a subset of the integers. This identity is a generalization of an identity…

Noncolliding Brownian motion (Dyson's Brownian motion model with parameter $\beta=2$) and noncolliding Bessel processes are determinantal processes; that is, their space-time correlation functions are represented by determinants. Under a…

In this paper, we introduce a two-parameters determinantal point process in the Poincar\'e disc and compute the asymptotics of the variance of its number of particles inside a disc centered at the origin and of radius $r$ as $r$ tends to…

We study the eigenvalue behaviour of large complex correlated Wishart matrices near an interior point of the limiting spectrum where the density vanishes (cusp point), and refine the existing results at the hard edge as well. More…

We consider the local field dynamical temperature correlation function of the Quantum Nonlinear Schrodinger equation with the finite coupling constant. This correlation function admits a Fredholm determinant representation. The related…

The logarithmic derivative of a point process plays a key role in the general approach, due to the third author, to constructing diffusions preserving a given point process. In this paper we explicitly compute the logarithmic derivative for…

We consider determinantal Coulomb gas ensembles with a class of discrete rotational symmetric potentials whose droplets consist of several disconnected components. Under the insertion of a point charge at the origin, we derive the…

These lectures present a survey of recent developments in the area of random matrices (finite and infinite) and random permutations. These probabilistic problems suggest matrix integrals (or Fredholm determinants), which arise very…

In a previous work, we proved an index theorem for families of asymptotically hyperbolic discrete dynamical systems and obtained applications to bifurcation theory. A weaker and far more common assumption than asymptotic hyperbolicity is…

It is known that determinantal point processes have an intimate relation to operator algebras. In the paper, we extend this relationship to encompass dynamical aspects. Especially, we delve into two types of determinantal point processes.…

We prove an exponential estimate for the asymptotics of Bergman kernels of a positive line bundle under hypotheses of bounded geometry. We give further Bergman kernel proofs of complex geometry results, such as separation of points,…

We study the emptiness formation probability (EFP) in the six-vertex model with domain wall boundary conditions. We present a conjecture according to which at the ice point, i.e., when all the Boltzmann weights are equal, the known multiple…

We show that the symplectic and orthogonal character analogues of Okounkov's Schur measure (on integer partitions) are determinantal, with explicit correlation kernels. We apply this to prove certain Borodin-Okounkov-Gessel-type results…

Determinantal point processes (DPPs) offer a powerful approach to modeling diversity in many applications where the goal is to select a diverse subset. We study the problem of learning the parameters (the kernel matrix) of a DPP from…

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.

We establish the asymptotics of the joint moments of the characteristic polynomial of a random unitary matrix and its derivative for general real values of the exponents, proving a conjecture made by Hughes in 2001. Moreover, we give a…