Stationary fluctuations for occupation times of the long-range voter models on lattices
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912599023550464 |
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| author | Xue, Xiaofeng |
| author_facet | Xue, Xiaofeng |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_17518 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stationary fluctuations for occupation times of the long-range voter models on lattices Xue, Xiaofeng Probability 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. |
| title | Stationary fluctuations for occupation times of the long-range voter models on lattices |
| topic | Probability |
| url | https://arxiv.org/abs/2509.17518 |