Stationary fluctuations for occupation times of the long-range voter models on lattices

2025/09/22 by Xiaofeng Xue, Xue, Xiaofeng
Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #FOS: Mathematics #Opinion Dynamics and Social Influence #Probability (math.PR) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2509.17518

openalex publication_date 2025/09/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we are concerned with the long-range voter model on lattices. We prove a stationary fluctuation theorem for the occupation time of the model under a proper time-space scaling. In several cases, the fluctuation limits are driven by fractional Brownian motions with Hurst parameters in (1/2, 1). The proof of our main result utilizes the martingale decomposition strategy introduced in \citeKipnis1987. A local central limit theorem of the long-range random walk, the duality relationship between the model and the long-range coalescing random walk and a fluctuation theorem of the empirical density field of the model play the key roles in the proof.

Related

• Long range voter models and dynamical fractional Brownian motion
• Sample path central limit theorem for the occupation time of the voter model on a lattice
• Occupation times of long-range exclusion and connections to KPZ class exponents
• Fluctuations of the occupation times for branching system starting from infinitely divisible point processes
• The mean field stubborn voter model