The spectrum of a random geometric graph is concentrated

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dc.creatorRai, Sanatan
dc.date2004-08-09
dc.date2004-09-23
dc.date.accessioned2026-07-07T05:11:07Z
dc.date.available2026-07-07T05:11:07Z
dc.descriptionConsider $n$ points distributed uniformly in $[0,1]^d$. Form a graph by connecting two points if their mutual distance is no greater than $r(n)$. This gives a random geometric graph, $\gnrn$, which is connected for appropriate $r(n)$. We show that the spectral measure of the transition matrix of the simple random walk (\abbr{srw}) on $\gnrn$ is concentrated, and in fact converges to that of the graph on the deterministic grid.
dc.identifierhttps://arxiv.org/abs/math/0408103
dc.identifierhttp://arxiv.org/abs/math/0408103
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/72134
dc.subjectProbability
dc.subjectStatistical Mechanics
dc.subjectSpectral Theory
dc.subject60D05; 34L20
dc.titleThe spectrum of a random geometric graph is concentrated
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