Integrated density of states for ergodic random Schrodinger operators on manifolds

被引：13

作者：

Peyerimhoff, N ^{[1
]}

Veselic, I ^{[1
]}

机构：

[1] Ruhr Univ Bochum, Fak Math, D-44780 Bochum, Germany

来源：

GEOMETRIAE DEDICATA | 2002年 / 91卷 / 01期

基金：

新加坡国家研究基金会;

关键词：

integrated density of states; random Schrodinger operators; Riemannian manifolds with compact quotient; amenable groups; ergodic theorem;

D O I：

10.1023/A:1016222913877

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider the Riemannian universal covering of a compact manifold M = X/Gamma and assume that Gamma is amenable. We show the existence of a (nonrandom) integrated density of states for an ergodic random family of Schrodinger operators on X.

引用

页码：117 / 135

页数：19

共 50 条

[1] Integrated Density of States for Ergodic Random Schrödinger Operators on Manifolds
Norbert Peyerimhoff
Ivan Veselić
Geometriae Dedicata, 2002, 91 : 117 - 135
[2] The integrated density of states for random schrodinger operators
Kirsch, Werner
Metzger, Bernd
SPECTRAL THEORY AND MATHEMATICAL PHYSICS: A FESTSCHRIFT IN HONOR OF BARRY SIMON'S 60TH BIRTHDAY: ERGODIC SCHRODINGER OPERATORS, SINGULAR SPECTRUM, ORTHOGONAL POLYNOMIALS, AND INVERSE SPECTRAL THEORY, 2007, 76 : 649 - 696
[3] The density of states and the spectral shift density of random Schrodinger operators
Kostrykin, V
Schrader, R
REVIEWS IN MATHEMATICAL PHYSICS, 2000, 12 (06) : 807 - 847
[4] Dependence of the density of states outer measure on the potential for deterministic Schrodinger operators on graphs with applications to ergodic and random models
Hislop, Peter D.
Marx, Christoph A.
JOURNAL OF FUNCTIONAL ANALYSIS, 2021, 281 (09)
[5] Uniform existence of the integrated density of states for random Schrodinger operators on metric graphs over Zd
Gruber, Michael J.
Lenz, Daniel H.
Veselic, Ivan
JOURNAL OF FUNCTIONAL ANALYSIS, 2007, 253 (02) : 515 - 533
[6] Some Estimates Regarding Integrated Density of States for Random Schrodinger Operator with Decaying Random Potentials
Dolai, Dhriti Ranjan
SPECTRAL THEORY AND MATHEMATICAL PHYSICS, 2016, 254 : 119 - 132
[7] Lp-Approximation of the Integrated Density of States for Schrodinger Operators with Finite Local Complexity
Gruber, Michael J.
Lenz, Daniel H.
Veselic, Ivan
INTEGRAL EQUATIONS AND OPERATOR THEORY, 2011, 69 (02) : 217 - 232
[8] The uniqueness of the integrated density of states for the Schrodinger operators for the robin boundary conditions
Mine, T
PUBLICATIONS OF THE RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES, 2002, 38 (02) : 355 - 385
[9] Spectra of random operators with absolutely continuous integrated density of states
del Rio, Rafael
JOURNAL OF MATHEMATICAL PHYSICS, 2014, 55 (04)
[10] Continuity properties of the integrated density of states on manifolds
Lenz, Daniel
Peyerimhoff, Norbert
Post, Olaf
Veselic, Ivan
JAPANESE JOURNAL OF MATHEMATICS, 2008, 3 (01): : 121 - 161

← 1 2 3 4 5 →