{"paper":{"title":"Anomalies in local Weyl laws and applications to random topology at critical dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.SP","authors_text":"Alejandro Rivera","submitted_at":"2016-11-07T12:28:19Z","abstract_excerpt":"Let $\\mathcal{M}$ be a smooth manifold of positive dimension $n$ equipped with a smooth density $d\\mu_{\\mathcal{M}}$. Let $A$ be a polyhomogeneous elliptic pseudo-differential operator of positive order $m$ on $\\mathcal{M}$ which is symmetric for the $L^2$ scalar product defined by $d\\mu_{\\mathcal{M}}$. For each $L>0$, the space $U_L=\\bigoplus_{\\lambda\\leq L}Ker(A-\\lambda Id)$ is a finite dimensional subspace of $C^\\infty(\\mathcal{M})$. Let $\\Pi_L$ be the spectral projector onto $U_L$. Given $s\\in\\mathbb{R}$, we compute the asymptotics of the integral kernel $K_L$ of $\\Pi_LA^{-s}$ in the cases"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.02018","kind":"arxiv","version":2},"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"}