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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.17518 |
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Table of Contents:
- 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 \cite{Kipnis1987}. 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.