Glauber dynamics in the continuum via generating functionals evolution

TL;DR

This paper develops a mathematical framework using generating functionals to describe the time evolution of Glauber dynamics in infinite particle systems, with potential extensions to global solutions and applications to Vlasov scaling.

Contribution

It introduces a novel approach using Banach space scales and Ovsjannikov-type results to analyze Glauber dynamics in the continuum.

Findings

Established local-in-time solutions for the dynamics.

Extended the method to Vlasov-type scaling scenarios.

Provided conditions for potential global-in-time solutions.

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.