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Abstract
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We consider the
facilitated exclusion process, which is a nonergodic, kinetically
constrained exclusion process. We show that in the hydrodynamic limit, its
macroscopic behavior is governed by a free boundary problem. The particles evolve
on the one-dimensional lattice according to jump rates which are degenerate, since
they can vanish on nontrivial configurations and create distinct phases: indeed,
configurations can be totally
blocked (they cannot evolve under the dynamics),
ergodic (they belong to an irreducible component), or
transient (after a
transitive period of time they will become either blocked or ergodic). We
additionally prove that the microscopic separation into blocked/ergodic phases fully
coincides with the moving interface problem given by the hydrodynamic
equation.
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Keywords
hydrodynamic limits, kinetically constrained exclusion
process, active-absorbing phase transition, Stefan problem
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Mathematical Subject Classification 2010
Primary: 35R35, 60J27, 60K35
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Milestones
Received: 17 February 2020
Revised: 8 October 2020
Accepted: 27 October 2020
Published: 16 March 2021
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