Mathematics – Probability
Scientific paper
2011-07-15
Mathematics
Probability
36 pages, 2 figures
Scientific paper
We consider two models of one-dimensional discrete random Schrodinger operators (H_n \psi)_l ={\psi}_{l-1}+{\psi}_{l +1}+v_l {\psi}_l, {\psi}_0={\psi}_{n+1}=0 in the cases v_k=\sigma {\omega}_k/\sqrt{n} and v_k=\sigma {\omega}_k/ \sqrt{k}. Here {\omega}_k are independent random variables with mean 0 and variance 1. We show that the eigenvectors are delocalized and the transfer matrix evolution has a scaling limit given by a stochastic differential equation. In both cases, eigenvalues near a fixed bulk energy E have a point process limit. We give bounds on the eigenvalue repulsion, large gap probability, identify the limiting intensity and provide a central limit theorem. In the second model, the limiting processes are the same as the point processes obtained as the bulk scaling limits of the beta-ensembles of random matrix theory. In the first model, the eigenvalue repulsion is much stronger.
Kritchevski Evgenij
Valkó Benedek
Virag Balint
No associations
LandOfFree
The scaling limit of the critical one-dimensional random Schrodinger operator does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The scaling limit of the critical one-dimensional random Schrodinger operator, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The scaling limit of the critical one-dimensional random Schrodinger operator will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-226330