Invariant measures of Mass Migration Processes

Abstract : We introduce the Mass Migration Process (MMP), a conservative particle system on ℕℤd. It consists in jumps of k particles (k≥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.
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Article dans une revue
Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2016, 21 (60), pp.1-52. 〈http://www.imstat.org/ejp/〉. 〈10.1214/16-EJP4399〉
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https://hal.archives-ouvertes.fr/hal-01172112
Contributeur : Thierry Gobron <>
Soumis le : lundi 6 juillet 2015 - 18:39:54
Dernière modification le : mardi 10 octobre 2017 - 11:22:04

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Lucie Fajfrovà, Thierry Gobron, Ellen Saada. Invariant measures of Mass Migration Processes. Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2016, 21 (60), pp.1-52. 〈http://www.imstat.org/ejp/〉. 〈10.1214/16-EJP4399〉. 〈hal-01172112〉

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