Vertex degree of random geometric graph on exponentially distributed points
作者： Bhupendra Gupta
DOI: 10.1016/J.SPL.2009.06.011
关键词:
摘要: Abstract In this article, we consider exponential random geometric graph, in d -dimensional space ( ≥ 2 ) . The main results are almost-sure asymptotic rates of convergence/divergence for the maximum and minimum vertex degrees when edge distance varies with number vertices.
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sci-hub.se 参考文章(13)
Mathew Penrose, Random Geometric Graphs ,(2003)
Béla Bollobás, Graph Theory: An Introductory Course ,(1979)
Srikanth K. Iyer, Bhupender Gupta, A Strong Law for the Largest Nearest-Neighbor Link on Normally Distributed Points arXiv: Probability. ,(2006)
Topological properties of the one dimensional exponential random geometric graph Random Structures and Algorithms. ,vol. 32, pp. 181- 204 ,(2008) , 10.1002/RSA.V32:2
Holger Rootzén, Holger Rootzén, Tailen Hsing, Extremes on trees Annals of Probability. ,vol. 33, pp. 413- 444 ,(2005) , 10.1214/009117904000001008
Martin J. B. Appel, Ralph P. Russo, The Maximum Vertex Degree of a Graph on Uniform Points in [0, 1]d Advances in Applied Probability. ,vol. 29, pp. 567- 581 ,(1997) , 10.2307/1428076
Mathew D. Penrose, Extremes for the minimal spanning tree on normally distributed points Advances in Applied Probability. ,vol. 30, pp. 628- 639 ,(1998) , 10.1239/AAP/1035228120
Bhupender Gupta, Srikanth K. Iyer, CRITICALITY OF THE EXPONENTIAL RATE OF DECAY FOR THE LARGEST NEAREST-NEIGHBOR LINK IN RANDOM GEOMETRIC GRAPHS Advances in Applied Probability. ,vol. 42, pp. 631- 658 ,(2010) , 10.1239/AAP/1282924057
Robert J. Serfling, Approximation Theorems of Mathematical Statistics ,(1980)
Michel Loève, Probability theory ,(1963)