Related papers: Asymptotics of a cubic sine kernel determinant

In Mombeni et al. (2019), Birnbaum-Saunders and Weibull kernel estimators were introduced for the estimation of cumulative distribution functions (c.d.f.s) supported on the half-line $[0,\infty)$. They were the first authors to use…

The main result of this paper is that determinantal point processes on the real line corresponding to projection operators with integrable kernels are quasi-invariant, in the continuous case, under the group of diffeomorphisms with compact…

In this paper, we study the asymptotic behavior of a family of pole-free solutions to the noncommutative Painlev\'e II equation. These particular solutions can be expressed in terms of the Fredholm determinant of the matrix version of the…

Let $(-A,B,C)$ be a linear system in continuous time $t>0$ with input and output space ${\mathbb C}^2$ and state space $H$. The scattering functions $\phi_{(x)}(t)=Ce^{-(t+2x)A}B$ determines a Hankel integral operator $\Gamma_{\phi_{(x)}}$;…

We obtain uniform asymptotics for polynomials orthogonal on a fixed and varying arc of the unit circle with a positive analytic weight function. We also complete the proof of the large $s$ asymptotic expansion for the Fredholm determinant…

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…

We prove that matrix Fredholm determinants related to multi-time processes can be expressed in terms of determinants of integrable kernels \`a la Its-Izergin-Korepin-Slavnov (IIKS) and hence related to suitable Riemann-Hilbert problems,…

The level spacing distributions which arise when one rescales the Laguerre or Jacobi ensembles of hermitian matrices is studied. These distributions are expressible in terms of a Fredholm determinant of an integral operator whose kernel is…

We compute the full off-diagonal asymptotics of the equivariant and partial Bergman kernels associated with a circle action on a prequantized K\"ahler manifold with bounded geometry at infinity, then use these results to compute the…

We study the injective norm of random skew-symmetric tensors and the associated fermionic quantum states, a natural measure of multipartite entanglement for systems of indistinguishable particles. Extending recent advances on random quantum…

A Hilbert space embedding for probability measures has recently been proposed, with applications including dimensionality reduction, homogeneity testing, and independence testing. This embedding represents any probability measure as a mean…

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…

Let A denote the C*algebra of bounded operators on L2(R) generated by: (i) all multiplications a(M) by functions a\in C[-\infty,+\infty], (ii) all multiplications by 2\pi-periodic continuous functions and (iii) all Fourier multipliers…

We consider Fredholm determinants of the form identity minus product of spectral projections corresponding to isolated parts of the spectrum of a pair of self-adjoint operators. We show an identity relating such determinants to an integral…

The parameter imbedding method for the Fredholm equation converts it into an initial value problem in its parameter $\lambda$. We establish the method for general operator equations of the form $[I + \hat{f}(\lambda)]\psi = \phi $. It is…

We use the steepest descents method to study the integral kernel of a family of normal random matrix ensembles with eigenvalue distribution P_{N}(z_{1},...,z_{N}) = Z_{N}^{-1} e^{-N\Sigma_{i=1}^{N}V_{\alpha}(z_{i})}…

We study the behaviors of the relative Bergman kernel metrics on holomorphic families of degenerating hyperelliptic Riemann surfaces and their Jacobian varieties. Near a node or cusp, we obtain precise asymptotic formulas with explicit…

In this work, we provide a self-contained derivation of the spin-operator matrix elements in the fermionic basis, for the critical periodic Ising chain at a generic system length $N\in 2Z_{\ge 2}$. The approach relies on the near-Cauchy…

We show the index 0 Fredholm property of the spectral family of the azimuthal harmonics of the charged Klein-Gordon operator on general cosmological slowly accelerating and rotating charged black hole type spacetimes, including the De…

We introduce a general method for transforming the equations of motion following from a Das-Jevicki-Sakita Hamiltonian, with boundary conditions, into a boundary value problem in one-dimensional quantum mechanics. For the particular case of…