Front progression for the East model

Abstract

The East model is a one-dimensional, non-attractive interacting particle system with Glauber dynamics, in which a flip is prohibited at a site $x$ if the right neighbour $x+1$ is occupied. Starting from a configuration entirely occupied on the left half-line, we prove a law of large numbers for the position of the left-most zero (the front), as well as ergodicity of the process seen from the front. For want of attractiveness, the one-dimensional shape theorem is not derived by the usual coupling arguments, but instead by quantifying the local relaxation to the non-equilibrium invariant measure for the process seen from the front. This is the first proof of a shape theorem for a kinetically constrained spin model.

38 pages, 9 figures; typos corrected and some details added since the first version

References in corpus (1)

• The East model: recent results and new progresses

Cited by in corpus (7)

• Noisy Coupled Qubits: Operator Spreading and the Fredrickson-Andersen Model
• Front propagation versus bulk relaxation in the annealing dynamics of a kinetically constrained model of ultrastable glasses
• Relaxation to equilibrium of generalized East processes on ${\mathbb{Z}}^d$: Renormalization group analysis and energy-entropy competition
• Shape theorem for a one-dimensional growing particle system with a bounded number of occupants per site
• Exponential convergence to equilibrium in supercritical kinetically constrained models at high temperature
• Cutoff for the bidirectional East Process
• Mixing time bounds for oriented kinetically constrained spin models