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Pré-Publication, Document De Travail Année : 2021

Invariant measures for multilane exclusion process

Résumé

We consider the simple exclusion process on Z × {0, 1}, that is, an "horizontal ladder" composed of 2 lanes. Particles can jump according to a lane-dependent translation-invariant nearest neighbour jump kernel, i.e. "horizontally" along each lane, and "vertically" along the scales of the ladder. We prove that generically, the set of extremal invariant measures consists of (i) translation-invariant product Bernoulli measures; and, modulo translations along Z: (ii) at most two shock measures (i.e. asymptotic to Bernoulli measures at ±∞) with asymptotic densities 0 and 2; (iii) at most three shock measures with a density jump of magnitude 1. We fully determine this set for certain parameter values. In fact, outside degenerate cases, there is at most one shock measure of type (iii). The result can be partially generalized to vertically cyclic ladders with arbitrarily many lanes. For the latter, we answer an open question of [5] about rotational invariance of stationary measures.
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Dates et versions

hal-03235516 , version 1 (25-05-2021)
hal-03235516 , version 2 (16-09-2022)
hal-03235516 , version 3 (20-11-2023)

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Gidi Amir, Christophe Bahadoran, Ofer Busani, Ellen Saada. Invariant measures for multilane exclusion process. 2021. ⟨hal-03235516v1⟩
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