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2016 Invariant measures of mass migration processes
Lucie Fajfrová, Thierry Gobron, Ellen Saada
Electron. J. Probab. 21: 1-52 (2016). DOI: 10.1214/16-EJP4399

Abstract

We introduce the “mass migration process” (MMP), a conservative particle system on ${\mathbb N}^{{\mathbb Z}^d}$. It consists in jumps of $k$ particles ($k\geq 1$) between sites, with a jump rate depending only on the state of the system at the departure and arrival sites of the jump. It generalizes misanthropes processes, hence zero range and target processes. After the construction of MMP, our main focus is on its invariant measures. We derive necessary and sufficient conditions for the existence of translation invariant and invariant product probability measures. In the particular cases of asymmetric mass migration zero range and mass migration target dynamics, these conditions yield explicit solutions. If these processes are moreover attractive, we obtain a full characterization of all translation invariant, invariant probability measures. We also consider attractiveness properties (through couplings), condensation phenomena, and their links for MMP. We illustrate our results on many examples; we prove the coexistence of condensation and attractiveness in one of them.

Citation

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Lucie Fajfrová. Thierry Gobron. Ellen Saada. "Invariant measures of mass migration processes." Electron. J. Probab. 21 1 - 52, 2016. https://doi.org/10.1214/16-EJP4399

Information

Received: 1 July 2015; Accepted: 20 July 2016; Published: 2016
First available in Project Euclid: 30 September 2016

zbMATH: 1348.60137
MathSciNet: MR3563888
Digital Object Identifier: 10.1214/16-EJP4399

Subjects:
Primary: 60K35, 82C22

JOURNAL ARTICLE
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