On the total length of the random minimal directed spanning tree

DOI10.1239/aap/1151337075zbMath1098.60046arXivmath/0409201OpenAlexW3106276570MaRDI QIDQ5480003

Mathew D. Penrose, Andrew R. Wade

Publication date: 25 July 2006

Published in: Advances in Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0409201

zbMATH Keywords

phase transitionpoint processspanning treefixed-point equationnearest-neighbour graph

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Trees (05C05) Random graphs (graph-theoretic aspects) (05C80) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

Related Items (16)

Thin tails of fixed points of the nonhomogeneous smoothing transform ⋮ Gaussian approximation for rooted edges in a random minimal directed spanning tree ⋮ Fixed points of the smoothing transform: two-sided solutions ⋮ Central limit theorems for the radial spanning tree ⋮ The radial spanning tree of a Poisson point process ⋮ Laws of large numbers in stochastic geometry with statistical applications ⋮ The functional equation of the smoothing transform ⋮ Linear stochastic equations in the critical case ⋮ Explicit laws of large numbers for random nearest-neighbour-type graphs ⋮ A boundary corrected expansion of the moments of nearest neighbor distributions ⋮ Limit theorems for random spatial drainage networks ⋮ Asymptotic theory for the multidimensional random on-line nearest-neighbour graph ⋮ Traffic flow densities in large transport networks ⋮ Asymptotics of geometrical navigation on a random set of points in the plane ⋮ The Dickman–Goncharov distribution ⋮ The Smoothing Transform: A Review of Contraction Results

Uses Software

• Quicksort

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