The distribution of localization centers in some discrete random systems

Abstract

As a supplement of our previous work, we consider the localized region of the random Schroedinger operators on $l^2({\mathbf{Z}}^d)$ and study the point process composed of their eigenvalues and corresponding localization centers. For the Anderson model, we show that, this point process in the natural scaling limit converges in distribution to the Poisson process on the product space of energy and space. In other models with suitable Wegner-type bounds, we can at least show that any limiting point processes are infinitely divisible.

References in corpus (3)

• Simplicity of eigenvalues in the Anderson model
• The repulsion between localization centers in the Anderson model
• On the Mott formula for the a.c. conductivity and binary correlators in the strong localization regime of disordered systems

Cited by in corpus (8)

• Minami's estimate: beyond rank one perturbation and monotonicity
• Eigenvalue statistics for random Schrodinger operators with non rank one perturbations
• Spectral statistics for the discrete Anderson model in the localized regime
• Shape of eigenvectors for the decaying potential model
• Eigenfunction Statistics for Anderson Model with Hölder continuous single site Potential
• The scaling limit of eigenfunctions for 1d random Schrödinger operator
• Poisson statistics for 1d Schrödinger operators with random decaying potentials
• Global multiplicity bounds and Spectral Statistics Random Operators