Asymptotic Approximations of Integrals

Wong, R.

doi:10.1137/1.9780898719260

Cited by 486 publications

(499 citation statements)

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“…also section 3.4 below) truncated at N = 5. An asymptotic analysis of the integral I in (3.51) at large R confirms this Yukawa-like behavior: using a stationary phase approach, the relevant function to study is f (k) = ka −1 ω at k = 0 [37]. The asymptotic behavior at large R is strongly dependent on the behavior of the even derivatives of f (k) and in particular the existence of power-law behavior seems to be connected to non-zero even derivatives of this function.…”

Section: Jhep01(2014)138mentioning

confidence: 72%

Holographic collisions in confining theories

Cardoso

Matéos

Pani

et al. 2014

J. High Energ. Phys.

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Abstract:We study the gravitational dual of a high-energy collision in a confining gauge theory. We consider a linearized approach in which two point particles traveling in an AdSsoliton background suddenly collide to form an object at rest (presumably a black hole for large enough center-of-mass energies). The resulting radiation exhibits the features expected in a theory with a mass gap: late-time power law tails of the form t −3/2 , the failure of Huygens' principle and distortion of the wave pattern as it propagates. The energy spectrum is exponentially suppressed for frequencies smaller than the gauge theory mass gap. Consequently, we observe no memory effect in the gravitational waveforms. At larger frequencies the spectrum has an upward-stairway structure, which corresponds to the excitation of the tower of massive states in the confining gauge theory. We discuss the importance of phenomenological cutoffs to regularize the divergent spectrum, and the aspects of the full non-linear collision that are expected to be captured by our approach.

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Section: Jhep01(2014)138mentioning

confidence: 72%

Holographic collisions in confining theories

Cardoso

Matéos

Pani

et al. 2014

J. High Energ. Phys.

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“…In fact the saddle point method [2,14] is applicable to the Laplace inversion integral f r (t) = 1 2iπ…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

The Hartman-Watson Distribution Revisited: Asymptotics for Pricing Asian Options

Gerhold

2011

J. Appl. Probab.

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“…The integrals that appear in (14) are in a form compatible with applying Watson's lemma [28]. In fact, Watson's lemma can be applied directly to the denominator.…”

Section: Motivations For the Diffusion Approximationmentioning

confidence: 99%

Continuum Approximation of Invasion Probabilities

Borchering¹,

McKinley²

2018

Multiscale Model. Simul.

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Abstract. In the last decade there has been growing criticism of the use of stochastic differential equations to approximate discrete-state-space, continuous-time Markov chain population models. In particular, several authors have demonstrated the failure of Diffusion Approximation, as it is often called, to approximate expected extinction times for populations that start in a quasi-stationary state. In this work we investigate a related, but distinct, population dynamics property for which Diffusion Approximation is unreliable: invasion probabilities. We consider the situation in which a few individuals are introduced into a population and ask whether their collective lineage can successfully invade. Because the population count is so small during the critical period of success or failure, the process is intrinsically stochastic and discrete. In addition to demonstrating how and why the Diffusion Approximation fails in the large population limit, we contrast this analysis with that of a sometimes more successful alternative WKB-like approach. Through numerical investigations, we also study how these approximations perform in an important intermediate regime. Surprisingly, we find that there are times when the Diffusion Approximation performs well, particularly when parameters are near-critical and the population size is small to intermediate.

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Asymptotic Approximations of Integrals

Cited by 486 publications

References 0 publications

Holographic collisions in confining theories

Holographic collisions in confining theories

The Hartman-Watson Distribution Revisited: Asymptotics for Pricing Asian Options

Continuum Approximation of Invasion Probabilities

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