Scaling limit of fluctuations for the equilibrium Glauber dynamics in continuum

摘要: The Glauber dynamics investigated in this paper are spatial birth and death processes a continuous system having grand canonical Gibbs measure of Ruelle type as an invariant measure. We prove that such processes, when appropriately scaled, have scaling limit generalized Ornstein–Uhlenbeck process. First we convergence the corresponding Dirichlet forms. This requires only very weak assumptions. interaction potential ϕ has to be stable (S), integrable (I), assume low activity high temperature regime. Under slightly stronger integrability condition (I∞) conjecture on Percus–Yevick equation even can strong generators. Finally, scaled converge law. Here hardest part is show tightness (note cadlag sample path). For proof positive (P). limiting process then identified via associated martingale problem. above mentioned generators essential.