MODERATE DEVIATIONS IN TRIANGLE COUNT
MODERATE DEVIATIONS IN TRIANGLE COUNT
复制标题
三角形数量的适度偏差
DOI：
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发表时间：
2021
期刊：
影响因子：
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通讯作者：
C. Radin
中科院分区：
文献类型：
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作者：
C. Radin
本文证明了G（n，m）随机图中三角形个数的中偏差界，补充了Goldschmidt等人最近的结果. G（n，m）随机图中三角形密度的中偏差在中心极限定理和大偏差之间有定性的变化，Goldschmidt等人的结果推广了前者，我们的结果推广了后者;我们还推测了政权之间急剧变化的精确形式。我们的结果可以解释为有限尺寸效应的限制边三角形图中的相变。
We prove moderate deviations bounds for the number of triangles in a G(n,m) random graph, complementing recent results of Goldschmidt et al. The moderate deviations of triangle density in G(n,m) graphs change qualitatively between the regime of the central limit theorem and the regime of large deviations, with those of Goldschmidt et al. extending the former and our results extending the latter; we also conjecture a precise form of sharp change between the regimes. Our results can be interpreted as finite size effects in phase transitions in constrained edge-triangle graphs.