= Lévy family of graphs
{c}
{title2=$\alpha_n(\varepsilon)\to0$}
= Lévy family
{c}
{synonym}
A <Lévy family of graphs> consists of finite connected <graphs> with their uniform <probability measures> and <graph distances> divided by their diameters, whose <concentration of measure> functions vanish at every fixed positive normalized radius. Equivalently, every family occupying at least half the vertices has a radius-$\lfloor\varepsilon D_n\rfloor$ neighbourhood occupying a proportion tending to one, uniformly over such families. <Harper theorem> and <binomial distribution> tail bounds prove this for the <hypercube graphs>.
Back to article page
