Noise effects on Padé approximants and conformal maps<sup>*</sup>

Costin, Ovidiu; Dunne, Gerald V.; Meynig, Max

doi:10.1088/1751-8121/aca303

Cited by 4 publications

(1 citation statement)

References 38 publications

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“…Finally, it is important to determine how robust this method is to noisy input data. The effect of noise on numerical rational approximation has been studied in [12], where the authors study the effects of noise on conformal maps generated using Padé approximation, and in [28], where the authors study the effects of noise on rational approximations generated using the AAA algorithm. It would be valuable to use similar methods to study the effect of noise on exponential asymptotic analyses.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Exponential Asymptotics Using Numerical Rational Approximation in Linear Differential Equations

LUSTRI,

CREW,

CHAPMAN

2023

ANZIAM J.

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Singularly perturbed ordinary differential equations often exhibit Stokes’ phenomenon, which describes the appearance and disappearance of oscillating exponentially small terms across curves in the complex plane known as Stokes lines. These curves originate at singular points in the leading-order solution to the differential equation. In many important problems, it is impossible to obtain a closed-form expression for these leading-order solutions, and it is therefore challenging to locate these singular points. We present evidence that the analytic leading-order solution of a linear differential equation can be replaced with a numerical rational approximation using the adaptive Antoulas–Anderson (AAA) method. Despite such an approximation having completely different singularity types and locations, we show that the subsequent exponential asymptotic analysis accurately predicts the exponentially small behaviour present in the solution. For sufficiently small values of the asymptotic parameter, this approach breaks down; however, the range of validity may be extended by increasing the number of poles in the rational approximation. We present a related nonlinear problem and discuss the challenges that arise due to nonlinear effects. Overall, our approach allows for the study of exponentially small asymptotic effects without requiring an exact analytic form for the leading-order solution; this permits exponential asymptotic methods to be used in a much wider range of applications.

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Section: Conclusion and Discussionmentioning

confidence: 99%

Exponential Asymptotics Using Numerical Rational Approximation in Linear Differential Equations

LUSTRI,

CREW,

CHAPMAN

2023

ANZIAM J.

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Borel resummation of secular divergences in stochastic inflation

Honda

Jinno

Pinol

et al. 2023

J. High Energ. Phys.

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We make use of Borel resummation to extract the exact time dependence from the divergent series found in the context of stochastic inflation. Correlation functions of self-interacting scalar fields in de Sitter spacetime are known to develop secular IR divergences via loops, and the first terms of the divergent series have been consistently computed both with standard techniques for curved spacetime quantum field theory and within the framework of stochastic inflation. We show that Borel resummation can be used to interpret the divergent series and to correctly infer the time evolution of the correlation functions. In practice, we adopt a method called Borel-Padé resummation where we approximate the Borel transformation by a Padé approximant. We also discuss the singularity structures of Borel transformations and mention possible applications to cosmology.

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QCD critical point, Lee-Yang edge singularities, and Padé resummations

Başar

2024

Phys. Rev. C

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I analyze the trajectory of the Lee-Yang edge singularities of the QCD equation of state in the complex baryon chemical potential (μB) plane for different values of the temperature by using the recent lattice results for the Taylor expansion coefficients up to eighth order in μB and various resummation techniques that blend in Padé expansions and conformal maps. By extrapolating from this information, I estimate for the location of the QCD critical point: Tc≈100 MeV, μc≈580 MeV. I also estimate the crossover slope at the critical point to be α1≈9∘ and further constrain the nonuniversal mapping parameters between the three-dimensional Ising model and QCD equations of state. Published by the American Physical Society 2024

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Noise effects on Padé approximants and conformal maps^*

Cited by 4 publications

References 38 publications

Exponential Asymptotics Using Numerical Rational Approximation in Linear Differential Equations

Exponential Asymptotics Using Numerical Rational Approximation in Linear Differential Equations

Borel resummation of secular divergences in stochastic inflation

QCD critical point, Lee-Yang edge singularities, and Padé resummations

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Noise effects on Padé approximants and conformal maps*

Cited by 4 publications

References 38 publications

Exponential Asymptotics Using Numerical Rational Approximation in Linear Differential Equations

Exponential Asymptotics Using Numerical Rational Approximation in Linear Differential Equations

Borel resummation of secular divergences in stochastic inflation

QCD critical point, Lee-Yang edge singularities, and Padé resummations

Contact Info

Product

Resources

About

Noise effects on Padé approximants and conformal maps^*