Scaling limits of random normal matrix processes at singular boundary points

被引：25

作者：

Ameur, Yacin ^{[1
]}

Kang, Nam-Gyu ^{[2
]}

Makarov, Nikolai ^{[3
]}

Wennman, Aron ^{[4
]}

机构：

[1] Lund Univ, Fac Sci, Dept Math, POB 118, S-22100 Lund, Sweden

[2] Korea Inst Adv Study, Sch Math, 85 Hoegiro, Seoul 02455, South Korea

[3] CALTECH, Dept Math, Pasadena, CA 91125 USA

[4] Tel Aviv Univ, Sch Math Sci, IL-69978 Tel Aviv, Israel

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2020年 / 278卷 / 03期

基金：

瑞典研究理事会; 美国国家科学基金会;

关键词：

Random normal matrix; Singular boundary point; Scaling limit; Hard edge; ORTHOGONAL POLYNOMIALS; UNIVERSALITY; ENSEMBLES; WEAK;

D O I：

10.1016/j.jfa.2019.108340

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We introduce a method for taking microscopic limits of normal matrix ensembles and apply it to study the behaviour near certain types of singular points on the boundary of the droplet. Our investigation includes ensembles without restrictions near the boundary, as well as hard edge ensembles, where the eigenvalues are confined to the droplet. We establish in both cases existence of new types of determinantal point fields, which differ from those which can appear at a regular boundary point, or in the bulk. (C) 2019 Elsevier Inc. All rights reserved.

引用

页数：46

共 36 条

[1] Universality at Weak and Strong Non-Hermiticity Beyond the Elliptic Ginibre Ensemble [J].

Akemann, Gernot ;

Cikovic, Milan ;

Venker, Martin .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2018, 362 (03) :1111-1141

[2]

Ameur Y, ARXIV180408587

[3] MICROSCOPIC DENSITIES AND FOCK-SOBOLEV SPACES [J].

Ameur, Yacin ;

Seo, Seong-Mi .

JOURNAL D ANALYSE MATHEMATIQUE, 2019, 139 (01) :397-420

[4] Rescaling Ward Identities in the Random Normal Matrix Model [J].

Ameur, Yacin ;

Kang, Nam-Gyu ;

Makarov, Nikolai .

CONSTRUCTIVE APPROXIMATION, 2019, 50 (01) :63-127

[5] RANDOM NORMAL MATRICES AND WARD IDENTITIES [J].

Ameur, Yacin ;

Hedenmalm, Haakan ;

Makarov, Nikolai .

ANNALS OF PROBABILITY, 2015, 43 (03) :1157-1201

[6]

[Anonymous], 1961, The Plasma Dispersion Function

[7]

[Anonymous], ARXIV180806959

[8]

[Anonymous], 2012, THESIS

[9]

[Anonymous], 2004, Pure and applied mathematics series, DOI DOI 10.1103/PhysRevE.74.041119

[10]

[Anonymous], LECT NOTES MATH

← 1 2 3 4 →