Related papers: Calculation of asymptotic normalization coefficien…
Despite the advances in the development of numerical methods analytical approaches still play the key role on the way towards a deeper understanding of many-particle systems. In this regards, diagonalization schemes for Hamiltonians…
A very simple procedure to calculate eigenenergies of quantum anharmonic oscillators is presented. The method, exact but for numerical computations, consists merely in requiring the vanishing of the Wronskian of two solutions which are…
A method to obtain all-order asymptotic results for the coefficients of perturbative expansions in zero-dimensional quantum field is described. The focus is on the enumeration of the number of skeleton or primitive diagrams of a certain QFT…
In a general class of Bayesian nonparametric models, we prove that the posterior distribution can be asymptotically approximated by a Gaussian process. Our results apply to nonparametric exponential family that contains both Gaussian and…
Starting from a characterization of holomorphic functions in terms of a suitable mean value property, we build some nonlinear asymptotic characterizations for complex-valued solutions of certain nonlinear systems, which have to do with the…
Tuning parameters are parameters involved in an estimating procedure for the purpose of reducing the risk of some other estimator. Examples include the degree of penalization in penalized regression and likelihood problems, as well as the…
Asymptotically free renormalization group trajectories can be constructed in nonabelian Higgs models with the aid of generalized boundary conditions imposed on the renormalized action. We detail this construction within the languages of…
In this paper we describe a method to compute Generalized Polarization Tensors. These tensors are the coefficients appearing in the multipolar expansion of the steady state voltage perturbation caused by an inhomogeneity of constant…
In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we solve in the asymptotic long-time regime the master equation for two independent harmonic oscillators interacting with an…
In this paper, we study the asymptotics of the Hahn polynomials Q_n(x; {\alpha}, {\beta}, N) as the degree n grows to infinity, when the parameters {\alpha} and {\beta} are fixed and the ratio of n/N = c is a constant in the interval (0,…
Analytical complexity of quantum wavefunction whose argument is extended into the complex plane provides an important information about the potentiality of manifesting complex quantum dynamics such as time-irreversibility, dissipation and…
Approximate Bayesian computation (ABC) using a sequential Monte Carlo method provides a comprehensive platform for parameter estimation, model selection and sensitivity analysis in differential equations. However, this method, like other…
We examine the asymptotics of the moments of characteristic polynomials of $N\times N$ matrices drawn from the Hermitian ensembles of Random Matrix Theory, in the limit as $N\to\infty$. We focus in particular on the Gaussian Unitary…
We prove the two-dimensional analogue of the asymptotics for Toeplitz determinants with Fisher-Hartwig singularities, for general real symbols. This formula has applications to random normal matrices with complex spectra: (i) the…
We first show that the standard deviation error of quantum amplitude estimation is asymptotically lower bounded by approximately $1.28 L^{-1}$, where $L$ is the number of queries. Then we propose a generalized qubitization that can…
Asymptotic approximations to the zeros of Hermite and Laguerre polynomials are given, together with methods for obtaining the coefficients in the expansions. These approximations can be used as a standalone method of computation of Gaussian…
Asymptotic expansions are derived for solutions of the parabolic cylinder and Weber differential equations. In addition the inhomogeneous versions of the equations are considered, for the case of polynomial forcing terms. The expansions…
We present simple, user-friendly bounds for the expected operator norm of a random kernel matrix under general conditions on the kernel function $k(\cdot,\cdot)$. Our approach uses decoupling results for U-statistics and the non-commutative…
Uniform asymptotic approximations are obtained for the prolate spheroidal wave functions, in the high-frequency case. The results are obtained by an application of certain existing asymptotic solutions of differential equations, and involve…
We consider signal source localization from range-difference measurements. First, we give some readily-checked conditions on measurement noises and sensor deployment to guarantee the asymptotic identifiability of the model and show the…