{"paper":{"title":"Spectral Properties of the Discrete Random Displacement Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"G\\\"unter Stolz, Roger Nichols","submitted_at":"2010-08-06T20:00:17Z","abstract_excerpt":"We investigate spectral properties of a discrete random displacement model, a Schr\\\"odinger operator on $\\ell^2(\\Z^d)$ with potential generated by randomly displacing finitely supported single-site terms from the points of a sublattice of $\\Z^d$. In particular, we characterize the upper and lower edges of the almost sure spectrum. For a one-dimensional model with Bernoulli distributed displacements, we can show that the integrated density of states has a $1/\\log^2$-singularity at external as well as internal band edges."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.1266","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}