Kurtosis of height fluctuations in (1 + 1) dimensional KPZ dynamics

Singha, Tapas; Nandy, Malay K.

doi:10.1088/1742-5468/2015/05/p05020

Cited by 7 publications

(19 citation statements)

References 58 publications

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“…Since the dynamics is governed by a white noise following a Gaussian distribution, the lowest order approximation appeares to be influenced rather strongly by the Gaussian noise. A similar trend was observed in the one-loop perturbative calculation for kurtosis, namely, Q = 0.1523 [42] which is lower than the Baik-Rains value 0.2892. However the value for skewness via the perturbative scheme, namely, S = 0.3237 [41] is slightly lower than the Baik-Rains value 0.3594.…”

Section: Discussionsupporting

confidence: 83%

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Hyperskewness of (1 + 1)-dimensional KPZ height fluctuations

Singha¹,

Nandy²

2016

J. Stat. Mech.

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Abstract. We evaluate the fifth order normalized cumulant, known as hyperskewness, of height fluctuations dictated by the (1 + 1)-dimensional KPZ equation for the stochastic growth of a surface on a flat geometry in the stationary state. We follow a diagrammatic approach and invoke a renormalization scheme to calculate the fifth cumulant given by a connected loop diagram. This, together with the result for the second cumulant, leads to the hyperskewness value S = 0.0835.

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Section: Discussionsupporting

confidence: 83%

“…We shall find a renormalized equivalent of this bare quantity by means of a renormalization scheme employed earlier for the calculation of skewness and kurtosis [41,42]. We perform the internal frequency integration in Eq.…”

Section: The Fifth Cumulantmentioning

confidence: 99%

Hyperskewness of (1 + 1)-dimensional KPZ height fluctuations

Singha¹,

Nandy²

2016

J. Stat. Mech.

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“…A similar scheme was employed earlier for the calculation of skewness [40] and kurtosis [41] in the case of non-conserved interface growth governed by the (1 + 1)-dimensional KPZ equation. The amputated parts of the connected loop diagrams, namely, l 2 , l etc., for the second and third moments as shown in Figs.…”

Section: Discussionmentioning

confidence: 99%

“…Subsequently, we calculate the skewness of height fluctuations of the VLDS equation. A similar scheme was employed earlier for the calculation of skewness [40] and kurtosis [41] in the case of non-conserved interface growth governed by the (1 + 1)dimensional KPZ equation. The amputated parts of the connected loop diagrams, namely, l 2 , l…”

Section: Discussionmentioning

confidence: 99%

A renormalization scheme and skewness of height fluctuations in (1 + 1)-dimensional VLDS dynamics

Singha¹,

Nandy²

2016

J. Stat. Mech.

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Abstract. We study the (1 + 1)-dimensional Villain, Lai, and Das Sarma (VLDS) equation driven by a Gaussian white noise and implement a renormalization scheme without rescaling at one-loop order. Using a diagrammatic method, we calculate the renormalized second and third moments in the large-scale and long-time limits. The ensuing skewness value is S = −0.0441. This (negative) value is consistent with the numerical prediction of Das Sarma et al. [Phys. Rev. E 53 359 (1996)].

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“…where k n = − n−1 j=1 k j , ω n = − n−1 j=1 ω j . The function L n is perturbatively computed to one loop order [43][44][45][46] as L n = (2D)δ n,2 + L n,1 ,…”

Section: Cumulantsmentioning

confidence: 99%

Gaussian statistics as an emergent symmetry of the stochastic scalar Burgers equation

Rodríguez-Fernández

Cuerno

2019

Phys. Rev. E

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Symmetries play a conspicuous role in the large-scale behavior of critical systems. In equilibrium they allow to classify asymptotics into different universality classes and, out of equilibrium, they sometimes emerge as collective properties which are not explicit in the "bare" interactions. Here we elucidate the emergence of an up-down symmetry in the asymptotic behavior of the stochastic scalar Burgers equation in one and two dimensions, manifested by the occurrence of Gaussian fluctuations even within the time regime controlled by nonlinearities. This robustness of Gaussian behavior contradicts naive expectations, due to the detailed relation -including the lack of up-down symmetry-between Burgers equation and the Kardar-Parisi-Zhang equation, which paradigmatically displays non-Gaussian fluctuations described by Tracy-Widom distributions. We reach our conclusions via a dynamic renormalization group study of the field statistics, confirmed by direct evaluation of the field probability distribution function from numerical simulations of the dynamical equation.

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Kurtosis of height fluctuations in (1 + 1) dimensional KPZ dynamics

Cited by 7 publications

References 58 publications

Hyperskewness of (1 + 1)-dimensional KPZ height fluctuations

Hyperskewness of (1 + 1)-dimensional KPZ height fluctuations

A renormalization scheme and skewness of height fluctuations in (1 + 1)-dimensional VLDS dynamics

Gaussian statistics as an emergent symmetry of the stochastic scalar Burgers equation

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