Asymptotics for weighted minimal spanning trees on random points

DOI10.1016/S0304-4149(99)00068-XzbMath0997.60024OpenAlexW1973974944MaRDI QIDQ1613584

Joseph E. Yukich

Publication date: 29 August 2002

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0304-4149(99)00068-x

zbMATH Keywords

minimal spanning treessuperadditive processsubadditive processisoperimetry boundary functional

Mathematics Subject Classification ID

Trees (05C05) Random graphs (graph-theoretic aspects) (05C80) Strong limit theorems (60F15)

Related Items (11)

Weak laws of large numbers in geometric probability ⋮ Strong laws for Euclidean graphs with general edge weights ⋮ On the quadratic random matching problem in two-dimensional domains ⋮ Continuous approximation formulas for location problems ⋮ Rate of convergence of power-weighted Euclidean minimal spanning trees ⋮ Fractal dimension estimation with persistent homology: a comparative study ⋮ Minimum spanning trees of random geometric graphs with location dependent weights ⋮ An average case analysis of the minimum spanning tree heuristic for the power assignment problem ⋮ On the choice of weight functions for linear representations of persistence diagrams ⋮ Fractal dimension and the persistent homology of random geometric complexes ⋮ Multivariate spatial central limit theorems with applications to percolation and spatial graphs

Cites Work

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• The longest edge of the random minimal spanning tree
• The central limit theorem for Euclidean minimal spanning trees. I
• Probability theory of classical Euclidean optimization problems
• Asymptotic of power-weighted Euclidean functionals
• The RSW theorem for continuum percolation and the CLT for Euclidean minimal spanning trees
• The central limit theorem for weighted minimal spanning trees on random points
• Asymptotics for the Euclidean TSP with power weighted edges
• Asymptotics for Euclidean functionals with power-weighted edges
• A new look at independence

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