Spectral gap of sparse bistochastic matrices with exchangeable rows

doi:10.1214/20-AIHP1065

CSpace

	Spectral gap of sparse bistochastic matrices with exchangeable rows
	Bordenave, Charles 1,2; Qiu, Yanqi 3,4,5,6; Zhang, Yiwei 7
	2020-11-01
发表期刊	ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES
ISSN	0246-0203
卷号	56 期号:4 页码:2971-2995
摘要	We consider a random bistochastic matrix of size n of the form MQ where M is a uniformly distributed permutation matrix and Q is a given bistochastic matrix. Under sparsity and regularity assumptions on Q, we prove that the second largest eigenvalue of MQ is essentially bounded by the normalized Hilbert-Schmidt norm of Q when n grows large. We apply this result to random walks on random regular digraphs.
关键词	Spectral gap Random bistochastic matrices High trace method Tangled-free paths
DOI	10.1214/20-AIHP1065
收录类别	SCI
语种	英语
资助项目	French ANR[ANR-16-CE40-0024-01] ; National Natural Science Foundation of China[NSFC Y7116335K1] ; National Natural Science Foundation of China[NSFC 11688101] ; National Science Foundation of China[NSFC 11701200] ; National Science Foundation of China[NSFC 11871262] ; Department of mathematics at Southern University of Science and Technology
WOS研究方向	Mathematics
WOS类目	Statistics & Probability
WOS记录号	WOS:000582036900027
出版者	INST MATHEMATICAL STATISTICS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/52386
专题	中国科学院数学与系统科学研究院
通讯作者	Bordenave, Charles
作者单位	1.CNRS, Inst Math Marseille, 39 Rue Frederic Joliot Curie, F-13013 Marseille, France 2.Aix Marseille Univ, 39 Rue Frederic Joliot Curie, F-13013 Marseille, France 3.Chinese Acad Sci, AMSS, Inst Math, Beijing 100190, Peoples R China 4.Chinese Acad Sci, Hua Loo Keng Key Lab Math, Inst Math, Beijing 100190, Peoples R China 5.Inst Math Toulouse, CNRS, Toulouse, France 6.Univ Toulouse 3, Toulouse, France 7.Huazhong Univ Sci & Technol, Ctr Math Sci, Sch Math & Stat, Hubei Key Lab Engn Modeling & Sci Comp, Wuhan 430074, Peoples R China
推荐引用方式 GB/T 7714	Bordenave, Charles,Qiu, Yanqi,Zhang, Yiwei. Spectral gap of sparse bistochastic matrices with exchangeable rows[J]. ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES,2020,56(4):2971-2995.
APA	Bordenave, Charles,Qiu, Yanqi,&Zhang, Yiwei.(2020).Spectral gap of sparse bistochastic matrices with exchangeable rows.ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES,56(4),2971-2995.
MLA	Bordenave, Charles,et al."Spectral gap of sparse bistochastic matrices with exchangeable rows".ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES 56.4(2020):2971-2995.