In infinite spin systems with noise on a single particle, unique invariant and periodic measures exist on finite subsystems and extend to the full lattice via tightness and weak convergence.
Zegarlinski , The strong decay to equilibrium for the stochastic dynamics of unbounded spin systems on a lattice , Commun
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Invariant and periodic measures in classical spin systems on infinite lattices with highly degenerate noise
In infinite spin systems with noise on a single particle, unique invariant and periodic measures exist on finite subsystems and extend to the full lattice via tightness and weak convergence.