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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.17778 |
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| _version_ | 1866911397147836416 |
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| author | Xiaofeng, Xue |
| author_facet | Xiaofeng, Xue |
| contents | In this paper, we extend the central limit theorem of the additive functional of the nearest-neighbor zero-range process given in \cite{Quastel2002} to the long-range case. Our main results show that in several cases the limit processes are driven by fractional Brownian motions with Hurst parameters in $(1/2, 3/4]$. A local central limit theorem of the long-range random walk and a relaxation to equilibrium theorem of the long-range zero-range process play the key roles in the proofs of our main results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_17778 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Central limit theorems for additive functionals of long-range zero-range processes Xiaofeng, Xue Probability In this paper, we extend the central limit theorem of the additive functional of the nearest-neighbor zero-range process given in \cite{Quastel2002} to the long-range case. Our main results show that in several cases the limit processes are driven by fractional Brownian motions with Hurst parameters in $(1/2, 3/4]$. A local central limit theorem of the long-range random walk and a relaxation to equilibrium theorem of the long-range zero-range process play the key roles in the proofs of our main results. |
| title | Central limit theorems for additive functionals of long-range zero-range processes |
| topic | Probability |
| url | https://arxiv.org/abs/2601.17778 |