One-Dimensional Geometric Random Graphs With Nonvanishing Densities—Part I: A Strong Zero-One Law for Connectivity

摘要: We consider a collection of n independent points which are distributed on the unit interval [0,1] according to some probability distribution function F. Two nodes said be adjacent if their distance is less than given threshold value. When F admits nonvanishing density f , we show under weak continuity assumption that property graph connectivity for induced geometric random exhibits strong zero-one law, and identify corresponding critical scaling. This achieved by generalizing nonuniform distributions limit result obtained Levy maximal spacings uniform distribution.