Central limit theorems for additive functionals of long-range zero-range processes
Probability
2026-01-27 v1
Abstract
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 . 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.
Keywords
Cite
@article{arxiv.2601.17778,
title = {Central limit theorems for additive functionals of long-range zero-range processes},
author = {Xue Xiaofeng},
journal= {arXiv preprint arXiv:2601.17778},
year = {2026}
}