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• W2016034145 abstract "Attractiveness is a fundamental tool to study interacting particle systems and the basic coupling construction is a usual route to prove this property, as for instance in simple exclusion. The derived Markovian coupled process $(xi_t,zeta_t)_{tgeq 0}$ satisfies: (A) if $xi_0leqzeta_0$ (coordinate-wise), then for all $tgeq 0$, $xi_tleqzeta_t$ a.s. In this paper, we consider generalized misanthrope models which are conservative particle systems on $Z^d$ such that, in each transition, $k$ particles may jump from a site $x$ to another site $y$, with $kgeq 1$. These models include simple exclusion for which $k=1$, but, beyond that value, the basic coupling construction is not possible and a more refined one is required. We give necessary and sufficient conditions on the rates to insure attractiveness; we construct a Markovian coupled process which both satisfies (A) and makes discrepancies between its two marginals non-increasing. We determine the extremal invariant and translation invariant probability measures under general irreducibility conditions. We apply our results to examples including a two-species asymmetric exclusion process with charge conservation (for which $kle 2$) which arises from a Solid-on-Solid interface dynamics, and a stick process (for which $k$ is unbounded) in correspondence with a generalized discrete Hammersley-Aldous-Diaconis model. We derive the hydrodynamic limit of these two one-dimensional models." @default.
• W2016034145 created "2016-06-24" @default.
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• W2016034145 date "2010-11-01" @default.
• W2016034145 modified "2023-09-23" @default.
• W2016034145 title "Couplings, attractiveness and hydrodynamics for conservative particle systems" @default.
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• W2016034145 doi "https://doi.org/10.1214/09-aihp347" @default.
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