Glauber dynamics in the continuum via generating functionals evolution

Abstract

We construct the time evolution for states of Glauber dynamics for a spatial infinite particle system in terms of generating functionals. This is carried out by an Ovsjannikov-type result in a scale of Banach spaces, leading to a local (in time) solution which, under certain initial conditions, might be extended to a global one. An application of this approach to Vlasov-type scaling in terms of generating functionals is considered as well.

24 pages

References in corpus (3)

• Spatial birth and death processes as solutions of stochastic equations
• Vlasov scaling for stochastic dynamics of continuous systems
• Correlation functions evolution for the Glauber dynamics in continuum

Cited by in corpus (7)

• On an aggregation in birth-and-death stochastic dynamics
• Dynamical Widom-Rowlinson model and its mesoscopic limit
• Statistical dynamics of continuous systems: perturbative and approximative approaches
• Linear evolution equations in scales of Banach spaces
• Around Ovsyannikov's method
• Nonlinear perturbations of evolution systems in scales of Banach spaces
• Weak-coupling limit for ergodic environments