An approximative approach to construction of the Glauber dynamics in continuum

TL;DR

This paper introduces a novel method for constructing Glauber dynamics in continuum spaces, proving the existence of a contraction semigroup and providing finite- and infinite-volume approximations.

Contribution

It presents a new approach to construct Glauber dynamics in continuum and establishes the existence of the associated semigroup with approximation methods.

Findings

Existence of a strongly continuous contraction semigroup is proven.

Finite- and infinite-volume approximations of the semigroup are developed.

The approach advances the mathematical understanding of continuum Glauber dynamics.

Abstract

We develop a new approach for the construction of the Glauber dynamics in continuum. Existence of the corresponding strongly continuous contraction semigroup in a proper Banach space is shown. Additionally we present the finite- and infinite-volume approximations of the semigroup by families of bounded linear operators.