---
格式版本: 2
标题: "Anomalous current fluctuations in the stochastic XNOR hopping model"
原文链接: "https://arxiv.org/abs/2608.10536"
发布日期: "2026-08-11"
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去重键: "https://arxiv.org/abs/2608.10536"
---

## Condensed Matter > Statistical Mechanics

## Title:Anomalous current fluctuations in the stochastic XNOR hopping model

Authors:[Balázs Pozsgay](https://arxiv.org/search/cond-mat?searchtype=author&query=Pozsgay,+B)

[View PDF](https://arxiv.org/pdf/2608.10536) [HTML (experimental)](https://arxiv.org/html/2608.10536v1)

> 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 $t^{1/4}$ 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.

| Comments: |  |
| --- | --- |
| Subjects: | Statistical Mechanics (cond-mat.stat-mech); Probability (math.PR); Exactly Solvable and Integrable Systems (nlin.SI) |
| Cite as: | [arXiv:2608.10536](https://arxiv.org/abs/2608.10536) \[cond-mat.stat-mech\] |
|  | (or [arXiv:2608.10536v1](https://arxiv.org/abs/2608.10536v1) \[cond-mat.stat-mech\] for this version) |
|  | [https://doi.org/10.48550/arXiv.2608.10536](https://doi.org/10.48550/arXiv.2608.10536) |

## Submission history

From: Balazs Pozsgay \[[view email](https://arxiv.org/show-email/18a47e57/2608.10536)\]  
**\[v1\]** Tue, 11 Aug 2026 06:16:37 UTC (89 KB)

[Which authors of this paper are endorsers?](https://arxiv.org/auth/show-endorsers/2608.10536) | Disable MathJax ([What is MathJax?](https://info.arxiv.org/help/mathjax.html))
