Related papers: Saddle-point integration of $C_\infty$ "bump" func…

Let $X$ be a complete, simply connected harmonic manifold of purely exponential volume growth. This class contains all non-flat harmonic manifolds of non-positive curvature and, in particular all known examples of harmonic manifolds except…

In this paper, we extend the functional approach for calculating the EFT likelihood by applying the saddle-point expansion. We demonstrate that, after suitable reformulation, the likelihood expression is consistent with the path integral…

We demonstrate a phenomenon of condensation of the Fourier transform $\widehat{f}$ of a function $f$ defined on the real line $\mathbb{R}$ which decreases rapidly on one half of the line. For instance, we prove that if $f$ is…

We calculate the false-vacuum decay rate in one-dimensional quantum mechanics on the basis of the saddle-point approximation in the Euclidean path integral at finite temperature. The saddle points are the finite-T and shifted bounce…

The use of hyperasymptotics and the Weniger transformation has been proposed, in a joint fashion, for decoding the divergent asymptotic series generated by the steepest descent on a wide class of saddle-point integrals {evaluated across…

Using existing, forward-in-time integration schemes, we demonstrate that it is possible to compute unstable, saddle-type fixed points of stiff systems of ODEs when the stable compenents are fast (i.e., rapidly damped) while the unstable…

An asymptotic analytical approach is proposed for bosonic probability amplitudes in unitary linear networks, such as the optical multiport devices for photons. The asymptotic approach applies for large number of bosons $N\gg M$ in the…

A version of the saddle point method is developed, which allows one to describe exactly the asymptotic behavior of distribution densities of Levy driven stochastic integrals with deterministic kernels. Exact asymptotic behavior is…

We consider the asymptotic evaluation of the integral transform $\int_0^\infty f(x) \, \sin^n(\lambda x)/x^n \,\text{d} x$ of an exponential type function $f(x)$ of type $\tau>0$, for large values of the parameter $\lambda$, where $n$ is a…

In this paper, we establish an improved version of a saddle point theorem ([4]) removing a weak lower semicontinuity assumption at all. We then revisit some of the applications of that theorem in the light of such an improvement. For…

We consider a fluid queue where the input process consists of N identical sources that turn on and off at exponential waiting times. The server works at the constant rate c and an on source generates fluid at unit rate. This model was first…

Ratios of quadratic forms in correlated normal variables which introduce noncentrality into the quadratic forms are considered. The denominator is assumed to be positive (with probability 1). Various serial correlation estimates such as…

The coefficients that appear in uniform asymptotic expansions for integrals are typically very complicated. In the existing literature the majority of the work only give the first two coefficients. In a limited number of papers where more…

It is shown that the atomic inversion in the Jaynes-Cummings model has an exact representation as an integral over the Hankel contour. For a field in a coherent state, the integral is evaluated using the saddle point method. The…

We derive tail asymptotics for the running maximum of the Cox-Ingersoll-Ross process. The main result is proved by the saddle point method, where the tail estimate uses a new monotonicity property of the Kummer function. This auxiliary…

We study the Fourier transform windowed by a bump function. We transfer Jackson's classical results on the convergence of the Fourier series of a periodic function to windowed series of a not necessarily periodic function. Numerical…

We consider the problem of finding critical points of functions that are non-convex and non-smooth. Studying a fairly broad class of such problems, we analyze the behavior of three gradient-based methods (gradient descent, proximal update,…

The asymptotic behavior of the convolution-integral of a special form of the Airy function and a function of the power-like behavior at infinity is obtained. The integral under consideration is the solution of the Cauchy problem for an…

The computation and inversion of the binomial and negative binomial cumulative distribution functions play a key role in many applications. In this paper, we explain how methods used for the central beta distribution function (described in…

We consider the uniform asymptotic expansion for the Gauss hypergeometric function \[F(a+\epsilon\lambda,m;c+\lambda;x),\qquad \lambda\to+\infty\] for $x<1$ and positive integer $m$ when the parameter $\epsilon>1$ and the constants $a$ and…