LLL and stochastic sandpile models

Jintai Ding Seungki Kim Tsuyoshi Takagi Yuntao Wang

Number Theory arXiv subject: Statistical Mechanics (cond-mat.stat-mech) mathscidoc:2207.24001

arXiv, 2020.3
The aim of the present paper is to suggest that statistical physics provides the correct language to understand the practical behavior of the LLL algorithm, most of which are left unexplained to this day. To this end, we propose sandpile models that imitate LLL with compelling accuracy, and prove for these models some of the most desired statements regarding LLL. We also formulate a few conjectures that formally capture our heuristics and would serve as milestones for further development of the theory.
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@inproceedings{jintai2020lll,
  title={LLL and stochastic sandpile models},
  author={Jintai Ding, Seungki Kim, Tsuyoshi Takagi, and Yuntao Wang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220722171134508618706},
  booktitle={arXiv},
  year={2020},
}
Jintai Ding, Seungki Kim, Tsuyoshi Takagi, and Yuntao Wang. LLL and stochastic sandpile models. 2020. In arXiv. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220722171134508618706.
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