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Large deviations for additive functionals of one-dimensional zero-range processes
Abstract
We prove a large deviation principle for additive functionals of local Lipschitz functions of a one-dimensional symmetric zero-range process on the diffusive scale. The rate function is obtained from the dynamical large deviation principle for the empirical density and is characterized by a variational constraint involving the density at a fixed spatial point. On the microscopic side, a super-exponential replacement is needed to replace the local observable with a function of the empirical density. On the macroscopic side, the spatial regularity enjoyed by finite-rate trajectories is needed to pass from spatial averages to point evaluation.
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BibTeX
@misc{seo2026large,
title = {{Large deviations for additive functionals of one-dimensional zero-range processes}},
author = {Insuk Seo and Kenkichi Tsunoda},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.12814},
eprint = {2610.12814},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.12814},
}
RIS
TY - UNPB
TI - Large deviations for additive functionals of one-dimensional zero-range processes
AU - Insuk Seo
AU - Kenkichi Tsunoda
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.12814
UR - https://arxiv.org/abs/2610.12814
AB - We prove a large deviation principle for additive functionals of local Lipschitz functions of a one-dimensional symmetric zero-range process on the diffusive scale. The rate function is obtained from the dynamical large deviation principle for the empirical density and is characterized by a variational constraint involving the density at a fixed spatial point. On the microscopic side, a super-exponential replacement is needed to replace the local observable with a function of the empirical density. On the macroscopic side, the spatial regularity enjoyed by finite-rate trajectories is needed to pass from spatial averages to point evaluation.
ER -