Inhomogeneous central limit theorems for the voter model occupation times

TL;DR

This paper extends central limit theorems for voter model occupation times to inhomogeneous initial distributions, utilizing duality and invariance principles to broaden understanding of these stochastic processes.

Contribution

It introduces inhomogeneous initial conditions into the functional central limit theorems for voter models, expanding prior homogeneous results.

Findings

Extended CLTs to inhomogeneous initial distributions

Utilized duality between voter model and coalescing random walk

Applied Donsker's invariance principle in proofs

Abstract

In this paper, we extend the functional central limit theorems for the occupation times of the voter models on lattices given in Xue2026 to the case where the initial distribution is a spatially inhomogeneous product measure. The duality relationship between the voter model and the coalescing random walk and the Donsker's invariance principle of the simple random walk play the key roles in the proofs of our main results.