Asymptotic expansions of the hypergeometric function with two large parameters—application to the partition function of a lattice gas in a field of traps

Cvitković, Mislav; Smith, Ana‐Sunčana; Pande, Jayant

doi:10.1088/1751-8121/aa7213

Cited by 19 publications

(12 citation statements)

References 59 publications

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“…Proof of lemma 10. Cvitković, Smith and Pande (2017) provides an asymptotic expansion of the hypergeometric function F in the case where the first and third parameters goes to infinity with a constant ratio. For a, c, z, ε ∈ R, b / ∈ Z \ N, such that ε > 1, and zε < 1, Cvitković, Smith and Pande (2017) gives in the section 2.2.2 (end of page 10)…”

Section: D1 Proof Of Intermediate Lemmasmentioning

confidence: 99%

SIRUS: Stable and Interpretable RUle Set for classification

Bénard¹,

Biau²,

Veiga³

et al. 2021

Electron. J. Statist.

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State-of-the-art learning algorithms, such as random forests or neural networks, are often qualified as "black-boxes" because of the high number and complexity of operations involved in their prediction mechanism. This lack of interpretability is a strong limitation for applications involving critical decisions, typically the analysis of production processes in the manufacturing industry. In such critical contexts, models have to be interpretable, i.e., simple, stable, and predictive. To address this issue, we design SIRUS (Stable and Interpretable RUle Set), a new classification algorithm based on random forests, which takes the form of a short list of rules. While simple models are usually unstable with respect to data perturbation, SIRUS achieves a remarkable stability improvement over cutting-edge methods. Furthermore, SIRUS inherits a predictive accuracy close to random forests, combined with the simplicity of decision trees. These properties are assessed both from a theoretical and empirical point of view, through extensive numerical experiments based on our R/C++ software implementation sirus available from CRAN.

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Section: D1 Proof Of Intermediate Lemmasmentioning

confidence: 99%

SIRUS: Stable and Interpretable RUle Set for classification

Bénard¹,

Biau²,

Veiga³

et al. 2021

Electron. J. Statist.

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“…The asymptotic large n behaviour can be obtained from the integral representation of the hypergeometric function, which at large n is dominated by a saddle-point (see e.g. [21]). This gives…”

Section: Generating Functional For the Free Partmentioning

confidence: 99%

Correlation functions in scalar field theory at large charge

Arias-Tamargo

Rodrı́guez-Gómez

Russo

2020

J. High Energ. Phys.

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We compute general higher-point functions in the sector of large charge operators φ n ,φ n at large charge in O(2) (φφ) 2 theory. We find that there is a special class of "extremal" correlators having only one insertion ofφ n that have a remarkably simple form in the doublescaling limit n → ∞ at fixed g n 2 ≡ λ, where g ∼ ǫ is the coupling at the O(2) Wilson-Fisher fixed point in 4 − ǫ dimensions. In this limit, also non-extremal correlators can be computed. As an example, we give the complete formula for φ(x 1 ) n φ(x 2 ) nφ (x 3 ) nφ (x 4 ) n , which reveals an interesting structure.

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“…This is straightforward. The leading term was computed for example in [44]. Extending this calculation to include fluctuations around the saddle point we get the asymptotic expansion…”

Section: Structure Of Singular Termsmentioning

confidence: 99%

Entropy and modular Hamiltonian for a free chiral scalar in two intervals

et al. 2018

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We calculate the analytic form of the vacuum modular Hamiltonian for a two interval region and the algebra of a current j(x) = ∂φ(x) corresponding to a chiral free scalar φ in d = 2. We also compute explicitly the mutual information between the intervals. This model shows a failure of Haag duality for two intervals that translates into a loss of a symmetry property for the mutual information usually associated with modular invariance. Contrary to the case of a free massless fermion, the modular Hamiltonian turns out to be completely non local. The calculation is done diagonalizing the density matrix by computing the eigensystem of a correlator kernel operator. These eigenvectors are obtained by a novel method that involves solving an equivalent problem for an holomorphic function in the complex plane where multiplicative boundary conditions are imposed on the intervals. Using the same technique we also re-derive the free fermion modular Hamiltonian in a more transparent way. arXiv:1809.00026v2 [hep-th]

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Asymptotic expansions of the hypergeometric function with two large parameters—application to the partition function of a lattice gas in a field of traps

Cited by 19 publications

References 59 publications

SIRUS: Stable and Interpretable RUle Set for classification

SIRUS: Stable and Interpretable RUle Set for classification

Correlation functions in scalar field theory at large charge

Entropy and modular Hamiltonian for a free chiral scalar in two intervals

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