Spectral statistics for one-dimensional Anderson model with unbounded but decaying potential

Authors

Anish Mallick, Tata Institute of Fundamental Research, Mumbai
Dhriti Ranjan Dolai, Indian Statistical Institute Bangalore

Article Type

Research Article

Publication Title

Infinite Dimensional Analysis, Quantum Probability and Related Topics

Abstract

In this work, we study the spectral statistics for Anderson model on 2(N) with decaying randomness whose single-site distribution has unbounded support. Here, we consider the operator Hω given by (Hωu) n = un+1 + un-1 + anωnun, an n-α and {ωn} are real i.i.d random variables following symmetric distribution μ with fat tail, i.e. μ((-R,R)c) < C Rfor R ≫ 1, for some constant C. In case of α -1 > 1 2, we are able to show that the eigenvalue process in (-2, 2) is the clock process.

DOI

10.1142/S0219025719500127

Publication Date

6-1-2019

Comments

Open Access, Green

Recommended Citation

Mallick, Anish and Dolai, Dhriti Ranjan, "Spectral statistics for one-dimensional Anderson model with unbounded but decaying potential" (2019). Journal Articles. 810.
https://digitalcommons.isical.ac.in/journal-articles/810