{"paper":{"title":"Asymptotic spectral distributions of distance $k$-graphs of star product graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.PR","authors_text":"Octavio Arizmendi, Tulio Gaxiola","submitted_at":"2014-08-25T08:51:50Z","abstract_excerpt":"Let $G$ be a finite connected graph and let $G^{[\\star N,k]}$ be the distance $k$-graph of the $N$-fold star power of $G$. For a fixed $k\\geq1$, we show that the large $N$ limit of the spectral distribution of $G^{[\\star N,k]}$ converges to a centered Bernoulli distribution, $1/2\\delta_{-1}+1/2\\delta_1$. The proof is based in a fourth moment lemma for convergence to a centered Bernoulli distribution."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.5682","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"}