The paper establishes the first finite-sample normal approximation bounds for the numbers of isolated edges and isolated 2-stars in uniform simple graphs with prescribed degrees, via new joint normal-Poisson Stein's method and indicator coupling.
Either Case (b4i): {t2, t3} ∩ {t′ 2, t′ 3}=∅or Case (b4ii):{t 2, t3} ∩ {t′ 2, t′ 3} ̸=∅happens
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Normal approximation of the numbers of isolated edges and isolated 2-stars in uniform simple graphs with given vertex degrees
The paper establishes the first finite-sample normal approximation bounds for the numbers of isolated edges and isolated 2-stars in uniform simple graphs with prescribed degrees, via new joint normal-Poisson Stein's method and indicator coupling.