A Note on the Distribution of the Extreme Degrees of a Random Graph Via the Stein-Chen Method
Copyright policy )A Note on the Distribution of the Extreme Degrees of a Random Graph Via the Stein-Chen Method
AbstractWe offer an alternative proof, using the Stein-Chen method, of Bollobás’ theorem concerning the distribution of the extreme degrees of a random graph. Our proof also provides a rate of convergence of the extreme degree to its asymptotic distribution. The same method also applies in a more general setting where the probability of every pair of vertices being connected by edges depends on the number of vertices.
- University of Maryland, College Park United States
- University of Maryland, Baltimore United States
- University of Maryland United States
total variation distance, Statistics of extreme values; tail inference, Probability (math.PR), Random graphs (graph-theoretic aspects), positive dependence, Mathematics - Statistics Theory, 05C80, 05C07, 62G32, Vertex degrees, Statistics Theory (math.ST), extremes, FOS: Mathematics, Mathematics - Combinatorics, Poisson approximation, Combinatorics (math.CO), random graphs, Mathematics - Probability
total variation distance, Statistics of extreme values; tail inference, Probability (math.PR), Random graphs (graph-theoretic aspects), positive dependence, Mathematics - Statistics Theory, 05C80, 05C07, 62G32, Vertex degrees, Statistics Theory (math.ST), extremes, FOS: Mathematics, Mathematics - Combinatorics, Poisson approximation, Combinatorics (math.CO), random graphs, Mathematics - Probability
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