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2018 Hydrodynamic limits for long-range asymmetric interacting particle systems
Sunder Sethuraman, Doron Shahar
Electron. J. Probab. 23: 1-54 (2018). DOI: 10.1214/18-EJP237

Abstract

We consider the hydrodynamic scaling behavior of the mass density with respect to a general class of mass conservative interacting particle systems on $\mathbb{Z} ^n$, where the jump rates are asymmetric and long-range of order $\|x\|^{-(n+\alpha )}$ for a particle displacement of order $\|x\|$. Two types of evolution equations are identified depending on the strength of the long-range asymmetry. When $0<\alpha <1$, we find a new integro-partial differential hydrodynamic equation, in an anomalous space-time scale. On the other hand, when $\alpha \geq 1$, we derive a Burgers hydrodynamic equation, as in the finite-range setting, in Euler scale.

Citation

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Sunder Sethuraman. Doron Shahar. "Hydrodynamic limits for long-range asymmetric interacting particle systems." Electron. J. Probab. 23 1 - 54, 2018. https://doi.org/10.1214/18-EJP237

Information

Received: 27 February 2018; Accepted: 17 October 2018; Published: 2018
First available in Project Euclid: 21 December 2018

zbMATH: 07021686
MathSciNet: MR3896867
Digital Object Identifier: 10.1214/18-EJP237

Subjects:
Primary: 60K35

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