发表机构
Yale University（耶鲁大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究针对含噪随机提升检测的假设检验问题，首次分析低次多项式阈值函数，得到含噪随机提升短环计数分布的新结果，推广了相关经典成果。
AI 中文摘要
在本研究中，我们针对从均匀随机d-正则图中检测基d-正则图的含噪随机提升这一自然假设检验问题，首次开展了低次多项式阈值函数的分析。在此过程中，我们得到了含噪随机提升中短环计数分布直至对数长度的新结果，该结果推广了McKay、Wormald与Wysocka以及Johnson在随机正则图情形下的成果，还有Fortin与Rudinsky在随机提升情形下的成果。
英文摘要
In this work, we present the first analysis of low-degree polynomial threshold functions for the natural hypothesis testing problem of detecting the noisy random lift of a base $d$-regular graph from a uniformly random $d$-regular graph. Along the way, we obtain a new result for the distribution of short cycle counts in noisy random lift up to logarithmic lengths, which generalizes results by McKay, Wormald, and Wysocka and by Johnson in the case of random regular graphs, and results by Greenhill, Janson, and Ruciński and by Fortin and Rudinsky in the case of random lifts.
Comments68 pages, 1 figure
