β-Laguerre随机矩阵最大特征值精确渐近性的一般结果
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摘要
利用β-Laguerre随机矩阵最大特征值的中心极限定理、尾概率不等式及广义β Tracy-Wisdom分布的性质,对于相当广泛的边界函数和拟权函数,得到了其最大特征值的矩完全收敛性的精确渐近性的一般结果.
By using the central limit theorem and the inequalities of the tail probability for the largest eigenvalue ofβ-Laguerre random matrix and properties of the generalβ Tracy-Wisdom distribution,we obtained a general result of precise asymptotics in complete moment convergence for the largest eigenvalue for more general boundary function and weighted function.
By using the central limit theorem and the inequalities of the tail probability for the largest eigenvalue ofβ-Laguerre random matrix and properties of the generalβ Tracy-Wisdom distribution,we obtained a general result of precise asymptotics in complete moment convergence for the largest eigenvalue for more general boundary function and weighted function.
引文
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[12]刘银萍.β-Hermite随机矩阵最大特征值精确渐近性的一般形式[J].吉林大学学报(理学版),2016,54(6):1328-1332.(LIU Yinping.A General Form on Precise Asymptotics for the Largest Eigenvalue ofβ-Hermite Random Matrix[J].Journal of Jilin University(Science Edition),2016,54(6):1328-1332.)
[13]张亚运,吴群英.φ-混合移动平均过程完全矩收敛的精确渐近性[J].吉林大学学报(理学版),2017,55(1):61-69.(ZHANG Yayun,WU Qunying.Precise Asymptotics of Complete Moment Convergence ofφ-Mixing Moving Average Process[J].Journal of Jilin University(Science Edition),2017,55(1):61-69.)
[14] ZHANG Yong,YANG Xiaoyun,DONG Zhishan.A General Law of Precise Asymptotics for the Complete Moment Convergence[J].Chin Ann Math(Ser B),2009,30(1):77-90.
[15] Hall P,Heyde C C.Martingale Limit Theory and Its Application[M].New York:Academic Press,1980.
[2] Geman S.A Limit Theorem for the Norm of Random Matrices[J].Ann Probab,1980,8(2):252-261.
[3] Johansson K.Shape Fluctuations and Random Matrices[J].Comm Math Phys,2000,209(2):437-476.
[4] Dumitriu I,Edelman A.Matrix Models for Beta Ensembles[J].J Math Phys,2002,43(11):5830-5847.
[5] Haagerup U,Thorbjrnsen S.Random Matrices with Complex Gaussian Entries[J].Exp Math,2003,21(4):293-337.
[6] Ledoux M,Rider B.Small Deviations for Beta Ensembles[J].Electron J Probab,2010,15(4):1319-1343.
[7] Ramírez J,Rider B,Virg B.Beta Ensembles,Stochastic Airy Spectrum and a Diffusion[J].J Amer Math Soc,2011,24(4):919-944.
[8] Gut A,Sptaru A.Precise Asymptotics in the Baum-Katz and Davis Law of Large Numbers[J].J Math Anal Appl,2000,248(1):233-246.
[9] SU Zhonggen.Precise Asymptotics for Random Matrices and Random Growth Models[J].Acta Math Sin(Engl Ser),2008,24(6):971-982.
[10] XIE Junshan.The Moment Convergence Rates for Largest Eigenvalues ofβEnsembles[J].Acta Math Sin(Engl Ser),2013,29(3):477-488.
[11] XIE Junshan,ZHAO Jing.A Result on Precise Asymptotics for Largest Eigenvalues ofβEnsembles[J/OL].J Inequal Appl,2014-10-16.https://doi.org/10.1186/1029-242x-2014-408.
[12]刘银萍.β-Hermite随机矩阵最大特征值精确渐近性的一般形式[J].吉林大学学报(理学版),2016,54(6):1328-1332.(LIU Yinping.A General Form on Precise Asymptotics for the Largest Eigenvalue ofβ-Hermite Random Matrix[J].Journal of Jilin University(Science Edition),2016,54(6):1328-1332.)
[13]张亚运,吴群英.φ-混合移动平均过程完全矩收敛的精确渐近性[J].吉林大学学报(理学版),2017,55(1):61-69.(ZHANG Yayun,WU Qunying.Precise Asymptotics of Complete Moment Convergence ofφ-Mixing Moving Average Process[J].Journal of Jilin University(Science Edition),2017,55(1):61-69.)
[14] ZHANG Yong,YANG Xiaoyun,DONG Zhishan.A General Law of Precise Asymptotics for the Complete Moment Convergence[J].Chin Ann Math(Ser B),2009,30(1):77-90.
[15] Hall P,Heyde C C.Martingale Limit Theory and Its Application[M].New York:Academic Press,1980.