正则方法与 Erdős--Rényi 超图的大偏差原理
Regularity method and large deviation principles for the Erdős--Rényi hypergraph
AI总结：
本文为随机超图建立定量大偏差理论，基于张量分解和新型割范数计数引理，精确刻画了 r-均匀 Erdős--Rényi 超图同态计数联合尾部渐近，并推广至诱导同态计数。
摘要：
我们为随机超图发展了一套定量的大偏差理论，该理论基于张量分解以及在一种新的割型范数族下的计数引理。作为主要应用，我们获得了任意固定 r≥2 的 r-均匀 Erdős--Rényi 超图中同态计数联合上尾和下尾的精确渐近，推广并改进了先前关于 Erdős--Rényi 图（r=2）的结果。该理论具有足够的定量性，允许超图的密度以多项式速率趋于零，并且还给出了其他非线性泛函（如诱导同态计数）的尾部渐近。
英文摘要：
We develop a quantitative large deviations theory for random hypergraphs, which rests on tensor decomposition and counting lemmas under a novel family of cut-type norms. As our main application, we obtain sharp asymptotics for joint upper and lower tails of homomorphism counts in the $r$-uniform Erdős--Rényi hypergraph for any fixed $r\ge 2$, generalizing and improving on previous results for the Erdős--Rényi graph ($r=2$). The theory is sufficiently quantitative to allow the density of the hypergraph to vanish at a polynomial rate, and additionally yields tail asymptotics for other nonlinear functionals, such as induced homomorphism counts.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
