REVIEW 1 cited by
Anderson-Bernoulli Localization on the 3D lattice and discrete unique continuation principle
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
Signed reviews
read the original abstract
We consider the Anderson model with Bernoulli potential on the 3D lattice, and prove localization of eigenfunctions corresponding to eigenvalues near zero, the lower boundary of the spectrum. We follow the framework by Bourgain-Kenig and Ding-Smart, and our main contribution is a 3D discrete unique continuation, which says that any eigenfunction of the harmonic operator with bounded potential cannot be too small on a significant fractional portion of all the points. Its proof relies on geometric arguments about the 3D lattice.
Forward citations
Cited by 1 Pith paper
-
Delocalization of One-Dimensional Random Band Matrices
For one-dimensional block band matrices with W > N^{1/2+c}, the paper proves the local semicircle law, eigenvector delocalization, quantum unique ergodicity, and GUE universality.
Discussion (0). Continue with ORCID to comment.