Abstract
We consider a version of continuum long-range percolation on finite boxes of in which the vertex set is given by the points of a Poisson point process and each pair of two vertices at distance r is connected with probability proportional to for a certain constant s. We explore the graph-theoretical distance in this model. The aim of this paper is to show that this random graph model undergoes phase transitions at values and in analogy to classical long-range percolation on , by using techniques which are based on an analysis of the underlying Poisson point process.
Acknowledgments
The author would like to thank the anonymous referees and the Editor for their constructive comments that improved the quality of this paper.
Citation
Ercan Sönmez. "Graph distances of continuum long-range percolation." Braz. J. Probab. Stat. 35 (3) 609 - 624, August 2021. https://doi.org/10.1214/21-BJPS500
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