Rescaling Ward Identities in the Random Normal Matrix Model

被引：30

作者：

Ameur, Yacin ^{[1
]}

Kang, Nam-Gyu ^{[2
]}

Makarov, Nikolai ^{[3
]}

机构：

[1] Lund Univ, Dept Math, Fac Sci, 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

来源：

CONSTRUCTIVE APPROXIMATION | 2019年 / 50卷 / 01期

基金：

美国国家科学基金会;

关键词：

Random normal matrix; Universality; Ward's equation; Translation invariance; LEVEL-SPACING DISTRIBUTIONS; DE-BRANGES SPACES; THEOREM;

D O I：

10.1007/s00365-018-9423-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study spacing distribution for the eigenvalues of a random normal matrix, in particular at points on the boundary of the spectrum. Our approach uses Ward's (or the rescaled loop) equationan identity satisfied by all sequential limits of the rescaled one-point functions.

引用

页码：63 / 127

页数：65

共 40 条

[1]

Ameur Y., RANDOM NORMAL MATRIX

[2]

Ameur Y., J ANAL MATH

[3] On Bulk Singularities in the Random Normal Matrix Model [J].

Ameur, Yacin ;

Seo, Seong-Mi .

CONSTRUCTIVE APPROXIMATION, 2018, 47 (01) :3-37

[4] A Density Theorem for Weighted Fekete Sets [J].

Ameur, Yacin .

INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2017, 2017 (16) :5010-5046

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

Ameur, Yacin ;

Hedenmalm, Haakan ;

Makarov, Nikolai .

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

[6] On a problem for Ward's equation with a Mittag-Leffler potential [J].

Ameur, Yacin ;

Kang, Nam-Gyu .

BULLETIN DES SCIENCES MATHEMATIQUES, 2013, 137 (07) :968-975

[7] FLUCTUATIONS OF EIGENVALUES OF RANDOM NORMAL MATRICES [J].

Ameur, Yacin ;

Hedenmalm, Hakan ;

Makarov, Nikolai .

DUKE MATHEMATICAL JOURNAL, 2011, 159 (01) :31-81

[8]

[Anonymous], ARXIV151008723

[9]

[Anonymous], ARXIV171006493

[10]

[Anonymous], 1924, Sitzungsber. Berl. Math. Ges

← 1 2 3 4 →