{"paper":{"title":"Asymptotic representation theory and the spectrum of a random geometric graph on a compact Lie group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Pierre-Lo\\\"ic M\\'eliot","submitted_at":"2018-02-27T18:52:37Z","abstract_excerpt":"Let $G$ be a compact Lie group, $N\\geq 1$ and $L>0$. The random geometric graph on $G$ is the random graph $\\Gamma(N,L)$ whose vertices are $N$ random points $g_1,\\ldots,g_N$ chosen under the Haar measure of $G$, and whose edges are the pairs $\\{g_i,g_j\\}$ with $d(g_i,g_j)\\leq L$, $d$ being the distance associated to the standard Riemannian structure on $G$. In this paper, we describe the asymptotic behavior of the spectrum of the adjacency matrix of $\\Gamma(N,L)$, when $N$ goes to infinity. If $L$ is fixed and $N \\to + \\infty$ (Gaussian regime), then the largest eigenvalues of $\\Gamma(N,L)$ c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.10071","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"}