Statistical dynamics of continuous systems: perturbative and approximative approaches

TL;DR

This paper explores Markov statistical dynamics in continuous systems, introducing perturbative and approximation methods for birth-death models and Glauber dynamics to better understand their evolution.

Contribution

It develops a perturbative technique for constructing statistical dynamics in continuum birth-death models and introduces a Markov chain approximation for Glauber dynamics.

Findings

Perturbative method effectively constructs dynamics for spatial birth-and-death models.

Markov chain approximation provides detailed insights into Glauber dynamics.

Applicable to a broad class of continuous stochastic systems.

Abstract

We discuss general concept of Markov statistical dynamics in the continuum. For a class of spatial birth-and-death models, we develop a perturbative technique for the construction of statistical dynamics. Particular examples of such systems are considered. For the case of Glauber type dynamics in the continuum we describe a Markov chain approximation approach that gives more detailed information about statistical evolution in this model.