On the continuity of the integrated density of states in the disorder

2019/03/28 by Shamis, Mira
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1903.12222

Abstract

Recently, Hislop and Marx studied the dependence of the integrated density of states on the underlying probability distribution for a class of discrete random Schrödinger operators, and established a quantitative form of continuity in weak* topology. We develop an alternative approach to the problem, based on Ky Fan inequalities, and establish a sharp version of the estimate of Hislop and Marx. We also consider a corresponding problem for continual random Schrödinger operators on \R^d.

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