{"paper":{"title":"Lifshitz Tails for Anderson Models with Sign-Indefinite Single-Site Potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Zhongwei Shen","submitted_at":"2013-06-13T19:30:18Z","abstract_excerpt":"We study the spectral minimum and Lifshitz tails for continuum random Schr\\\"{o}dinger operators of the form \\begin{equation*} H_{\\om}=-\\De+V_{0}+\\sum_{i\\in\\Z^{d}}\\om_{i}u(\\cdot-i), \\end{equation*} where $V_{0}$ is the periodic potential, $\\{\\om_{i}\\}_{i\\in\\Z^{d}}$ are i.i.d random variables and $u$ is the sign-indefinite impurity potential. Recently, this model has been proven to exhibit Lifshitz tails near the bottom of the spectrum under the small support assuption of $u$ and the reflection symmetry assumption of $V_{0}$ and $u$. We here drop the reflection symmetry assumption of $V_{0}$ and"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.3205","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"}