The spectral edge of some random band matrices

被引：62

作者：

Sodin, Sasha ^{[1
]}

机构：

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

来源：

ANNALS OF MATHEMATICS | 2010年 / 172卷 / 03期

关键词：

SAMPLE COVARIANCE-MATRIX; LARGEST EIGENVALUES; UNIVERSALITY; ENSEMBLES; GRAPHS;

D O I：

10.4007/annals.2010.172.2223

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the asymptotic distribution of the eigenvalues of random Hermitian periodic band matrices, focusing on the spectral edges. The eigenvalues close to the edges converge in distribution to the Airy point process if (and only if) the band is sufficiently wide (W >> N-5/6). Otherwise, a different limiting distribution appears.

引用

页码：2223 / 2251

页数：29

共 35 条

[1] Non-backtracking random walks mix faster [J].

Alon, Noga ;

Benjamini, Itai ;

Lubetzky, Eyal ;

Sodin, Sasha .

COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 2007, 9 (04) :585-603

[2]

[Anonymous], 1971, INDEPENDENT STATIONA

[3] LIMIT OF THE SMALLEST EIGENVALUE OF A LARGE DIMENSIONAL SAMPLE COVARIANCE-MATRIX [J].

BAI, ZD ;

YIN, YQ .

ANNALS OF PROBABILITY, 1993, 21 (03) :1275-1294

[4] Edge scaling limits for a family of non-Hermitian random matrix ensembles [J].

Bender, Martin .

PROBABILITY THEORY AND RELATED FIELDS, 2010, 147 (1-2) :241-271

[5]

Bogachev L.V., 1991, Mat. Zametki, V50, P31

[6]

Bogachev L. V, 1991, MAT ZAMETKI, V50, P157

[7] Density of states for random band matrices [J].

Disertori, M ;

Pinson, H ;

Spencer, T .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2002, 232 (01) :83-124

[8]

ERDOS L, ARXIV10021695

[9]

ERDOS L, ARXIV10051838

[10]

FELDHEIM ON, GEOM FUNCT IN PRESS

← 1 2 3 4 →