LARGE DEVIATIONS FOR TOP EIGENVALUES OF ß -JACOBI ENSEMBLES AT SCALING TEMPERATURES∗

LARGE DEVIATIONS FOR TOP EIGENVALUES OF ß -JACOBI ENSEMBLES AT SCALING TEMPERATURES^∗

LARGE DEVIATIONS FOR TOP EIGENVALUES OF ß -JACOBI ENSEMBLES AT SCALING TEMPERATURES^∗

LARGE DEVIATIONS FOR TOP EIGENVALUES OF ß -JACOBI ENSEMBLES AT SCALING TEMPERATURES^∗

LARGE DEVIATIONS FOR TOP EIGENVALUES OF ß -JACOBI ENSEMBLES AT SCALING TEMPERATURES^∗

摘要/Abstract

参考文献

Metrics

本文评价

推荐阅读 10

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 13

Metrics

本文评价

推荐阅读 10

doi:10.1007/s10473-023-0418-7

数学物理学报(英文版) ›› 2023, Vol. 43 ›› Issue (4): 1767-1780.doi: 10.1007/s10473-023-0418-7

Liangzhen LEI¹, Yutao MA^2,†

1. School of Mathematical Science, Capital Normal University, Beijing 100048, China;
2. School of Mathematical Sciences & Laboratory of Mathematics and Complex Systems of Ministry of Education, Beijing Normal University, Beijing 100875, China

收稿日期:2022-04-02 修回日期:2022-10-22 发布日期:2023-08-08
通讯作者: †Yutao MA, E-mail: mayt@bnu.edu.cn
作者简介:Liangzhen, LEI E-mail: leiliangzhen@cnu.edu.cn
基金资助:
*Ma's research was supported by the NSFC (12171038, 11871008) and 985 Projects.

Liangzhen LEI¹, Yutao MA^2,†

1. School of Mathematical Science, Capital Normal University, Beijing 100048, China;
2. School of Mathematical Sciences & Laboratory of Mathematics and Complex Systems of Ministry of Education, Beijing Normal University, Beijing 100875, China

Received:2022-04-02 Revised:2022-10-22 Published:2023-08-08
Contact: †Yutao MA, E-mail: mayt@bnu.edu.cn
About author:Liangzhen, LEI E-mail: leiliangzhen@cnu.edu.cn
Supported by:
*Ma's research was supported by the NSFC (12171038, 11871008) and 985 Projects.

摘要： Let $\lambda=(\lambda_1, \cdots, \lambda_n)$ be $\beta$ -Jacobi ensembles with parameters $p_1, p_2, n$ and $\beta,$ with $\beta$ varying with $n.$ Set $\gamma=\lim\limits_{n\rightarrow\infty}\frac{n}{p_1}$ and $\sigma=\lim\limits_{n\rightarrow\infty}\frac{p_1}{p_2}.$ Suppose that $\lim\limits_{n\to\infty}\frac{\log n}{\beta n}=0$ and $0\le \sigma\gamma< 1.$ We offer the large deviation for $\frac{p_1+p_2}{p_1}\max\limits_{1\le i\le n}\lambda_{i}$ when $\gamma>0$ via the large deviation of the corresponding empirical measure and via a direct estimate, respectively, when $\gamma=0.$

关键词: $\beta$ -Jacobi ensemble, large deviation, Wachter law, extremal eigenvalue

Abstract: Let $\lambda=(\lambda_1, \cdots, \lambda_n)$ be $\beta$ -Jacobi ensembles with parameters $p_1, p_2, n$ and $\beta,$ with $\beta$ varying with $n.$ Set $\gamma=\lim\limits_{n\rightarrow\infty}\frac{n}{p_1}$ and $\sigma=\lim\limits_{n\rightarrow\infty}\frac{p_1}{p_2}.$ Suppose that $\lim\limits_{n\to\infty}\frac{\log n}{\beta n}=0$ and $0\le \sigma\gamma< 1.$ We offer the large deviation for $\frac{p_1+p_2}{p_1}\max\limits_{1\le i\le n}\lambda_{i}$ when $\gamma>0$ via the large deviation of the corresponding empirical measure and via a direct estimate, respectively, when $\gamma=0.$

Key words: $\beta$ -Jacobi ensemble, large deviation, Wachter law, extremal eigenvalue

Liangzhen LEI, Yutao MA. LARGE DEVIATIONS FOR TOP EIGENVALUES OF ß -JACOBI ENSEMBLES AT SCALING TEMPERATURES^∗[J]. 数学物理学报(英文版), 2023, 43(4): 1767-1780.

Liangzhen LEI, Yutao MA. LARGE DEVIATIONS FOR TOP EIGENVALUES OF ß -JACOBI ENSEMBLES AT SCALING TEMPERATURES^∗[J]. Acta mathematica scientia,Series B, 2023, 43(4): 1767-1780.

[1] Anderson G, Guionnet A, Zeitouni O.An Introduction to Random Matrices. Cambridge: Cambridge University Press, 2010
[2] Dumitriu I, Paquette E. Global fluctuations for linear statistics of

β

$\beta$ -Jacobi ensembles. Random Matrices: Theor Appl, 2012, 1(4): 1250013
[3] Féral D. On large deviations for the spectral measure of discrete Coulomb gas//Donati-Martin C, Emery M, Rouault A, Stricker C. Séminaire de Probabilités XLI. 1934 of Lecture Notes in Mathematics. Berlin: Springer, 2008: 19-49
[4] Forrester P J.Log-Gases and Random Matrices. Princeton: Princeton University Press, 2010
[5] Gamboa F, Rouault A. Large deviations for random spectral measures and sum rules. Appl Math Res eXpress, 2011, 2: 281-307
[6] Huang N, Ma Y T. Limit theorems for

β

$\beta$ -Laguerre and

β

$\beta$ -Jacobi ensembles. Acta Math Sci, 2022, 42B(6): 2025-2039
[7] Jiang T. Limit theorems for beta-Jacobi ensembles. Bernoulli, 2013, 19(3): 1028-1046
[8] Ma Y T.Unified limits and large deviation principles for

β

$\beta$ -Laguerre ensembles in global regime. To appear at Acta Math Sinica
[9] Ma Y T.Limits theorems and large deviations for

β

$\beta$ -Jacobi ensembles at scaling temperatures. To appear at Acta Math Sinica
[10] Nagel J. Nonstandard limit theorems and large deviations for the Jacobi beta ensembles. Random Matrices: Theor Appl, 2014, 3(3): 1450012
[11] Pakzad C. Large deviations principle for the largest eigenvalue of the Gaussian

β

$\beta$ -Ensemble at high temperature. J Theoret Probab, 2018, 33: 428-443
[12] Trinh K D. On spectral measures of random Jacobi matrices. Osaka J Math, 2018, 55: 595-617
[13] Yang R Y.Large Deviations of the Extreme Eigenvalues of Classical Beta Ensembles[D]. Beijing: Beijing Normal University, 2021

Viewed

Full text

	From	local

	Times	6
	Rate	100%

Abstract

100

Just accepted	Online first	Issue

0	0	100

	From	Others

	Times	100
	Rate	100%

Cited

Web of Science	Crossref	ScienceDirect	Search for Citations in Google Scholar >>


This page requires you have already subscribed to WoS.

Shared

Discussed

[1]	Fen HE, Zhen WANG, Tingting CHEN. THE SHOCK WAVES FOR A MIXED-TYPE SYSTEM FROM CHEMOTAXIS^∗[J]. 数学物理学报(英文版), 2023, 43(4): 1717 -1734 .
[2]	Yanyan CUI, Zunfeng LI, Yonghong XIE, Yuying QIAO. THE NONLINEAR BOUNDARY VALUE PROBLEM FOR k HOLOMORPHIC FUNCTIONS IN $\mathbb{C}^2$ ^∗[J]. 数学物理学报(英文版), 2023, 43(4): 1571 -1586 .
[3]	Lili FAN, Meichen HOU. ASYMPTOTIC STABILITY OF SHOCK WAVES FOR THE OUTFLOW PROBLEM OF A HEAT-CONDUCTIVE IDEAL GAS WITHOUT VISCOSITY^∗[J]. 数学物理学报(英文版), 2023, 43(4): 1735 -1766 .
[4]	Wei LUO, Zhaoyang YIN. LOCAL BIFURCATION OF STEADY ALMOST PERIODIC WATER WAVES WITH CONSTANT VORTICITY^∗[J]. 数学物理学报(英文版), 2023, 43(4): 1633 -1644 .
[5]	Fei WU, Zejun WANG, Fangqi CHEN. THE GLOBAL EXISTENCE OF BV SOLUTIONS OF THE ISENTROPIC p-SYSTEM WITH LARGE INITIAL DATA^∗[J]. 数学物理学报(英文版), 2023, 43(4): 1668 -1674 .
[6]	Jinxia CEN, Stanis law MIGÓRSKI, Emilio VILCHES, Shengda ZENG. TIME PERIODIC SOLUTIONS TO THE EVOLUTIONARY OSEEN MODEL FOR A GENERALIZED NEWTONIAN INCOMPRESSIBLE FLUID^∗[J]. 数学物理学报(英文版), 2023, 43(4): 1645 -1667 .
[7]	Zhenhai Liu, Nikolaos S. Papageorgiou. SINGULAR DOUBLE PHASE EQUATIONS^*[J]. 数学物理学报(英文版), 2023, 43(3): 1031 -1044 .
[8]	Lili WEN, Engui FAN, Yong CHEN. THE SASA-SATSUMA EQUATION ON A NON-ZERO BACKGROUND: THE INVERSE SCATTERING TRANSFORM AND MULTI-SOLITON SOLUTIONS^*[J]. 数学物理学报(英文版), 2023, 43(3): 1045 -1080 .
[9]	Qing Guo, Leiga Zhao. POSITIVE SOLUTIONS WITH HIGH ENERGY FOR FRACTIONAL SCHRÖDINGER EQUATIONS^*[J]. 数学物理学报(英文版), 2023, 43(3): 1116 -1130 .
[10]	Leilei CUI, Jiaxing GUO, Gongbao LI. THE EXISTENCE AND LOCAL UNIQUENESS OF MULTI-PEAK SOLUTIONS TO A CLASS OF KIRCHHOFF TYPE EQUATIONS^*[J]. 数学物理学报(英文版), 2023, 43(3): 1131 -1160 .

Just accepted

Online first

Just accepted

Online first

[1]	Ran Wang, Beibei Zhang. A LARGE DEVIATION PRINCIPLE FOR THE STOCHASTIC GENERALIZED GINZBURG-LANDAU EQUATION DRIVEN BY JUMP NOISE^*[J]. 数学物理学报(英文版), 2023, 43(2): 505-530.
[2]	黄春茂, 王晨, 王效强. MOMENTS AND LARGE DEVIATIONS FOR SUPERCRITICAL BRANCHING PROCESSES WITH IMMIGRATION IN RANDOM ENVIRONMENTS[J]. 数学物理学报(英文版), 2022, 42(1): 49-72.
[3]	胡淑兰, 李瑞囡, 王新宇. CENTRAL LIMIT THEOREM AND MODERATE DEVIATIONS FOR A CLASS OF SEMILINEAR STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS[J]. 数学物理学报(英文版), 2020, 40(5): 1477-1494.
[4]	李贺宇, 陈夏. PRECISE MOMENT ASYMPTOTICS FOR THE STOCHASTIC HEAT EQUATION OF A TIME-DERIVATIVE GAUSSIAN NOISE[J]. 数学物理学报(英文版), 2019, 39(3): 629-644.
[5]	高付清, 徐明周. RELATIVE ENTROPY AND LARGE DEVIATIONS UNDER SUBLINEAR EXPECTATIONS[J]. 数学物理学报(英文版), 2012, 32(5): 1826-1834.
[6]	刘莉, 万成高, 冯艳钦. LARGE DEVIATIONS AND MODERATE DEVIATIONS FOR SUMS OF NEGATIVELY EPENDENT RANDOM VARIABLES[J]. 数学物理学报(英文版), 2011, 31(1): 344-352.
[7]	高付清, 蒋辉, 汪宝彬. MODERATE DEVIATIONS FOR PARAMETER ESTIMATORS IN FRACTIONAL ORNSTEIN-UHLENBECK PROCESS[J]. 数学物理学报(英文版), 2010, 30(4): 1125-1133.
[8]	何晓霞; 高付清. MODERATE DEVIATIONS AND LARGE DEVIATIONS FOR A TEST OF SYMMETRY#br# BASED ON KERNEL DENSITY ESTIMATOR[J]. 数学物理学报(英文版), 2008, 28(3): 665-674.
[9]	胡舒合; 王学军. LARGE DEVIATIONS FOR SOME DEPENDENT SEQUENCES[J]. 数学物理学报(英文版), 2008, 28(2): 295-300.
[10]	胡亦钧; 明瑞星; 杨文权. LARGE DEVIATIONS AND MODERATE DEVIATIONS FOR m-NEGATIVELY ASSOCIATED RANDOM VARIABLES[J]. 数学物理学报(英文版), 2007, 27(4): 886-896.
[11]	沈思. LARGE DEVIATION FOR THE EMPIRICAL CORRELATION COEFFICIENT OF TWO GAUSSIAN RANDOM VARIABLES[J]. 数学物理学报(英文版), 2007, 27(4): 821-828.
[12]	王霞; 高付清. MODERATE DEVIATIONS FROM HYDRODYNAMIC LIMIT OF A GINZBURG-LANDAU MODEL[J]. 数学物理学报(英文版), 2006, 26(4): 691-701.
[13]	高付清. SMALL PERTURBATION CRAMER METHODS AND MODERATE DEVIATIONS FOR MARKOV PROCESSES[J]. 数学物理学报(英文版), 1995, 15(4): 394-405.