Large Deviations Principle for the Largest Eigenvalue of the Gaussian βdocumentclass[12pt]{minimal}usepackage{amsmath}usepackage{wasysym}usepackage{amsfonts}usepackage{amssymb}usepackage{amsbsy}usepackage{mathrsfs}usepackage{upgreek}setlength{oddsidemargin}{-69pt}egin{document}$$eta $$end{document}-Ensemble at High Temperature

Cambyse Pakzad

首页> 外文期刊>Journal of theoretical probability >Large Deviations Principle for the Largest Eigenvalue of the Gaussian βdocumentclass[12pt]{minimal}usepackage{amsmath}usepackage{wasysym}usepackage{amsfonts}usepackage{amssymb}usepackage{amsbsy}usepackage{mathrsfs}usepackage{upgreek}setlength{oddsidemargin}{-69pt}egin{document}$$eta $$end{document}-Ensemble at High Temperature

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Large Deviations Principle for the Largest Eigenvalue of the Gaussian βdocumentclass[12pt]{minimal}usepackage{amsmath}usepackage{wasysym}usepackage{amsfonts}usepackage{amssymb}usepackage{amsbsy}usepackage{mathrsfs}usepackage{upgreek}setlength{oddsidemargin}{-69pt}egin{document}$$eta $$end{document}-Ensemble at High Temperature

机译：Gaussianβ DocumentClass的最大特征值的大偏差原理[12pt] {minimal} usepackage {ammath} usepackage {kyysym} usepackage {amsfonts} usepackage {amssymb} usepackage {amsbsy} usepackage {mathrsfs} usepackage {supmeek} setLength { oddsidemargin} { - 69pt} begin {document} $$ beta $$ end {document} - 在高温下

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We consider the Gaussian βdocumentclass[12pt]{minimal}usepackage{amsmath}usepackage{wasysym}usepackage{amsfonts}usepackage{amssymb}usepackage{amsbsy}usepackage{mathrsfs}usepackage{upgreek}setlength{oddsidemargin}{-69pt}egin{document}$$eta $$end{document}-ensemble when βdocumentclass[12pt]{minimal}usepackage{amsmath}usepackage{wasysym}usepackage{amsfonts}usepackage{amssymb}usepackage{amsbsy}usepackage{mathrsfs}usepackage{upgreek}setlength{oddsidemargin}{-69pt}egin{document}$$eta $$end{document} scales with n (the number of particles) such that n-1?β?1documentclass[12pt]{minimal}usepackage{amsmath}usepackage{wasysym}usepackage{amsfonts}usepackage{amssymb}usepackage{amsbsy}usepackage{mathrsfs}usepackage{upgreek}setlength{oddsidemargin}{-69pt}egin{document}$$displaystyle {{n}^{-1}ll eta ll 1}$$end{document}. Under a certain regime for βdocumentclass[12pt]{minimal}usepackage{amsmath}usepackage{wasysym}usepackage{amsfonts}usepackage{amssymb}usepackage{amsbsy}usepackage{mathrsfs}usepackage{upgreek}setlength{oddsidemargin}{-69pt}egin{document}$$eta $$end{document}, we show that the largest particle satisfies a large deviations principle in Rdocumentclass[12pt]{minimal}usepackage{amsmath}usepackage{wasysym}usepackage{amsfonts}usepackage{amssymb}usepackage{amsbsy}usepackage{mathrsfs}usepackage{upgreek}setlength{oddsidemargin}{-69pt}egin{document}$$mathbb {R}$$end{document} with speed nβdocumentclass[12pt]{minimal}usepackage{amsmath}usepackage{wasysym}usepackage{amsfonts}usepackage{amssymb}usepackage{amsbsy}usepackage{mathrsfs}usepackage{upgreek}setlength{oddsidemargin}{-69pt}egin{document}$$neta $$end{document} and explicit rate function. As a consequence, the largest particle converges in probability to 2, the rightmost point of the semicircle law.

机译：我们考虑高斯β DocumentClass [12pt] {minimal} usepackage {ammath} usepackage {kyysym} usepackage {amsfonts} usepackage {amssymb} usepackage {amsbsy} usepackage {mathrsfs} usepackage {supmeek} setLength { oddsidemargin} { - 69pt} begin {document} $$ beta $$ end {document} - 当β documentclass [12pt] {minimal}时 usepackage {ammath} usepackage {kyysym} usepackage {amsfonts} usepackage {amssymb} usepackage {amsbsy} usepackage {mathrsfs} usepackage {supmeek} setLength { oddsidemargin} { - 69pt} begin {document} $$ beta $$ end {document}尺寸使用n（粒子的数量），使得n-1？β？1 documentclass [12pt] {minimal} usepackage {ammath} usepackage {kyysym} usepackage {amsfonts} usepackage {amssymb} usepackage {amsbsy} usepackage {mathrsfs} usepackage {supmeek} setLength { oddsidemargin} { - 69pt} begin {document} $$ displaystyle {{n} ^ { - 1} ll beta ll 1} $$ end {document}。在β DocumentClass的某个制度下[12pt] {minimal} usepackage {ammath} usepackage {kyysym} usepackage {amsfonts} usepackage {amssymb} usepackage {amsbsy} usepackage {mathrsfs} usepackage {supmeek} setLength { oddsidemargin} { - 69pt} begin {document} $$$ beta $$ end {document}，我们显示最大的粒子满足R DocumentClass [12pt] {minimal}中的大偏差原理。 usepackage {ammath} usepackage {kyysym} usepackage {amsfonts} usepackage {amssymb} usepackage {amsbsy} usepackage {mathrsfs} usepackage {supmeek} setLength { oddsidemargin} { - 69pt} begin {document} $$ natmbb {r} $$ end {document}速度nβ documentclass [12pt] {minimal} usepackage {ammath} usepackage {kyysym} usepackage {amsfonts} usepackage {amssymb} usepackage {amsbsy} usepackage {mathrsfs} usepackage {supmeek} setLength { oddsidemargin} { - 69pt} begin {document} $$ n beta $$ end {document}和显式速率函数。因此，最大的粒子会聚到2的概率，是半圆法的最右边点。

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《Journal of theoretical probability》 |2020年第1期|共16页
作者
Cambyse Pakzad;
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1grid.10992.330000 0001 2188 0914MAP 5 UMR CNRS 8145Université Paris DescartesParisFrance;

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正文语种 eng
中图分类概率论（几率论、或然率论）;
关键词
Large deviations principle; Random matrices; Gaussian βdocumentclass12pt{minimal}usepackage{amsmath}usepackage{wasysym}usepackage{amsfonts}usepackage{amssymb}usepackage{amsbsy}usepackage{mathrsfs}usepackage{upgreek}setlength{oddsidemargin}{-69pt}egin{document}$$eta $$end{document}-ensembles; Extreme eigenvalue; 60B20; 60F10;

机译：大偏差原理;随机矩阵;高斯β documentClass [12pt] {minimal} usepackage {ammath} usepackage {isysym} usepackage {amsfonts} usepackage {amssys} usepackage {amsbsy} usepackage {mathrsfs} usepackage { 升级} setLength { oddsidemargin} { - 69pt} begin {document} $$$ beta $$ end {document} -ensembles;极端特征值;60b20;60f10;

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