{"paper":{"title":"Asymptotic adaptive threshold for connectivity in a random geometric social network","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ahmed Sid-Ali, Khader Khadraoui","submitted_at":"2018-10-15T15:49:49Z","abstract_excerpt":"Consider a dynamic random geometric social network identified by $s_t$ independent points $x_t^1,\\ldots,x_t^{s_t}$ in the unit square $[0,1]^2$ that interact in continuous time $t\\geq 0$. The generative model of the random points is a Poisson point measures. Each point $x_t^i$ can be active or not in the network with a Bernoulli probability $p$. Each pair being connected by affinity thanks to a step connection function if the interpoint distance $\\|x_t^i-x_t^j\\|\\leq a_\\mathsf{f}^\\star$ for any $i\\neq j$. We prove that when $a_\\mathsf{f}^\\star=\\sqrt{\\frac{(s_t)^{l-1}}{p\\pi}}$ for $l\\in(0,1)$, t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.06479","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"}