{"paper":{"title":"Full Szeg\\H{o}-type trace asymptotics for ergodic operators on large boxes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.SP","authors_text":"Adrian Dietlein","submitted_at":"2017-09-30T13:54:17Z","abstract_excerpt":"We prove full Szeg\\H{o}-type large-box trace asymptotics for selfadjoint $\\mathbb{Z}^d$-ergodic operators $\\Omega\\ni \\omega\\mapsto H_\\omega$ acting on $L^2(\\mathbb{R}^d)$. More precisely, let $g$ be a bounded, compactly supported and real-valued function such that the (averaged) operator kernel of $g(H_\\omega)$ decays sufficiently fast, and let $h$ be a sufficiently smooth compactly supported function. We then prove a full asymptotic expansion of the averaged trace of the operator $h(g(H_\\omega)_{[-L,L]^d})$ in terms of the length-scale $L$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.00201","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"}