Integrated density of states for random metrics on manifolds

Lenz, D.; Peyerimhoff, N.; Veselic, I.

Abstract

This paper carries over the fundamental properties of random Schroedinger operators to random Laplace-Beltrami operators, that is, Laplacians with random metrics. Namely, we (A) discuss a framework for ergodic, random operators on covering manifolds with randomness entering both via potential and metrics, (B) show measurability of the introduced operators, which implies, in particular, almost sure constancy of their spectral features, (C) prove existence and the selfaveraging property of the integrated density of states together with a Pastur-Shubin type trace formula.

Citation

Lenz, D., Peyerimhoff, N., & Veselic, I. (2004). Integrated density of states for random metrics on manifolds. Proceedings of the London Mathematical Society, 88(3), 733-752. https://doi.org/10.1112/s0024611503014576

• Journal Article Type: Article
• Online Publication Date: May 1, 2004
• Publication Date: May 1, 2004
• Deposit Date: Apr 26, 2007
• Journal: Proceedings of the London Mathematical Society
• Print ISSN: 0024-6115
• Electronic ISSN: 1460-244X
• Publisher: Wiley
• Peer Reviewed: Peer Reviewed
• Volume: 88
• Issue: 3
• Pages: 733-752
• DOI: https://doi.org/10.1112/s0024611503014576
• Keywords: Integrated density of states, Random metrics, Random operators, Schrödinger operators on manifolds, Spectral density.