Spectra of Random Regular Hypergraphs
Spectra of Random Regular Hypergraphs
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DOI：
10.37236/8741
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发表时间：
2019-05
期刊：
影响因子：
--
通讯作者：
Ioana Dumitriu;Yizhe Zhu
中科院分区：
文献类型：
--
作者：
Ioana Dumitriu;Yizhe Zhu
本文研究了Feng和Li（1996）定义的正则超图的谱。我们的主要结果类似于Alon关于随机正则超图的谱隙的猜想。然后，我们将第二特征值与正则超图上的非回溯随机游动的扩张性质和混合率联系起来。我们还证明了Angelini等人（2015）中引入的随机正则超图的非回溯算子的谱间隙。最后，我们得到了随机正则超图的经验谱分布（ESD）在不同区域的收敛性。在某些条件下，我们可以显示ESD的本地法律。
In this paper, we study the spectra of regular hypergraphs following the definitions from Feng and Li (1996). Our main result is an analog of Alon's conjecture for the spectral gap of the random regular hypergraphs. We then relate the second eigenvalues to both its expansion property and the mixing rate of the non-backtracking random walk on regular hypergraphs. We also prove the spectral gap for the non-backtracking operator of a random regular hypergraph introduced in Angelini et al. (2015). Finally, we obtain the convergence of the empirical spectral distribution (ESD) for random regular hypergraphs in different regimes. Under certain conditions, we can show a local law for the ESD.