Non-Lifshitz tails at the spectral bottom of some random operators

摘要

In this paper we continue with the investigation of the behavior of the integrated density of states of random operators of the form H-omega = -del rho(omega)del. In the present work we are interested in its behavior at 0, the bottom of the spectrum of H-omega. We prove that it converges exponentially fast to the integrated density of states of some periodic operator (H) over bar. Being periodic, (H) over bar cannot exhibit a Lifshitz behaviour. This result relates to the result of S. M. Kozlov ( Russ. Math. Surv. 34( 4): 168 - 169, 1979) and improves it.