We give an alternative proof and improve upon a result of S.M. Kozlov \cite{ko}. It deals with the asymptotic of the integrated density of states of the acoustic operator $\displaystyle H_\omega=-\nabla\rho_\omega\nabla$, at the bottom of the spectrum.
Perturbations of the Landau Hamiltonian: Asymptotics of eigenvalue clusters
Asymptotics of the finite-temperature sine kernel determinant
Asymptotics of the determinant of the modified Bessel functions and the second Painlevé equation
