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Kinetically constrained models with random constraints. (English) Zbl 1446.82057
Summary: We study two kinetically constrained models in a quenched random environment. The first model is a mixed threshold Fredrickson-Andersen model on $$\mathbb{Z}^2$$, where the update threshold is either $$1$$ or $$2$$. The second is a mixture of the Fredrickson-Andersen $$1$$-spin facilitated constraint and the North-East constraint in $$\mathbb{Z}^2$$. We compare three time scales related to these models – the bootstrap percolation time for emptying the origin, the relaxation time of the kinetically constrained model, and the time for emptying the origin of the kinetically constrained model – and understand the effect of the random environment on each of them.
##### MSC:
 82C22 Interacting particle systems in time-dependent statistical mechanics 82C43 Time-dependent percolation in statistical mechanics 60K37 Processes in random environments 60K35 Interacting random processes; statistical mechanics type models; percolation theory
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