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Spectral gap of sparse bistochastic matrices with exchangeable rows
Bordenave, Charles1,2; Qiu, Yanqi3,4,5,6; Zhang, Yiwei7
2020-11-01
Source PublicationANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES
ISSN0246-0203
Volume56Issue:4Pages:2971-2995
AbstractWe 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.
KeywordSpectral gap Random bistochastic matrices High trace method Tangled-free paths
DOI10.1214/20-AIHP1065
Indexed BySCI
Language英语
Funding ProjectFrench 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 Research AreaMathematics
WOS SubjectStatistics & Probability
WOS IDWOS:000582036900027
PublisherINST MATHEMATICAL STATISTICS
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/52386
Collection中国科学院数学与系统科学研究院
Corresponding AuthorBordenave, Charles
Affiliation1.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
Recommended Citation
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.
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