Anomalous current fluctuations in the stochastic XNOR hopping model
Abstract
We consider fluctuations of the spin current in the stochastic XNOR process, a kinetically constrained hopping model in one spatial dimension. We formulate three conjectures with explicit amplitudes for the long-time current distributions: a Gaussian limit on the t1/4 scale for homogeneous initial states with nonzero magnetization, a half-normal limit on the t1/4 scale for domain-wall states with opposite magnetizations, and an M-Wright limit on the t1/8 scale for homogeneous initial states at zero magnetization. Earlier work identified the tracer mechanism and anticipated the scaling exponents and limiting shapes in the domain-wall and zero-magnetization settings. Starting from the microscopic XNOR dynamics, we predict the missing amplitudes for the continuous-time process and extend the picture to homogeneous biased initial data. Simulations provide numerical support for all three conjectures without fitted parameters. A separate mathematical companion paper presents an extensively AI-generated candidate proof. Generative-AI tools were used in the research and writing workflow.
Related
- Exact anomalous current fluctuations in the strong-anisotropy limit of the XXZ chain
- Universal classical and quantum fluctuations in the large deviations of current of noisy quantum systems: Quantum symmetric simple exclusion and inclusion processes
- Gaussian fluctuations for the stochastic wave equation with drift
- Density and Current Fluctuations for Run-and-Tumble Particles With and Without Interactions
- Fluctuations and multifractality in stochastic models of interface growth and population dynamics
BibTeX
@misc{pozsgay2026anomalous,
title = {{Anomalous current fluctuations in the stochastic XNOR hopping model}},
author = {Balázs Pozsgay},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.10536},
eprint = {2608.10536},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.10536},
}
RIS
TY - UNPB
TI - Anomalous current fluctuations in the stochastic XNOR hopping model
AU - Balázs Pozsgay
PY - 2026
DA - 2026/09/07
PB - arXiv
DO - 10.48550/arxiv.2608.10536
UR - https://arxiv.org/abs/2608.10536
AB - We consider fluctuations of the spin current in the stochastic XNOR process, a kinetically constrained hopping model in one spatial dimension. We formulate three conjectures with explicit amplitudes for the long-time current distributions: a Gaussian limit on the t^1/4 scale for homogeneous initial states with nonzero magnetization, a half-normal limit on the t^1/4 scale for domain-wall states with opposite magnetizations, and an M-Wright limit on the t^1/8 scale for homogeneous initial states at zero magnetization. Earlier work identified the tracer mechanism and anticipated the scaling exponents and limiting shapes in the domain-wall and zero-magnetization settings. Starting from the microscopic XNOR dynamics, we predict the missing amplitudes for the continuous-time process and extend the picture to homogeneous biased initial data. Simulations provide numerical support for all three conjectures without fitted parameters. A separate mathematical companion paper presents an extensively AI-generated candidate proof. Generative-AI tools were used in the research and writing workflow.
ER -