@inbook{ab69f4b4d1fb4d969debc60df115ed41,
title = "Geometric Random Graphs on Circles",
abstract = "Given a dense countable set in a metric space, the infinite random geometric graph is the random graph with the given vertex set and where any two points at distance less than 1 are connected, independently, with some fixed probability. It has been observed by Bonato and Janssen that in some, but not all, such settings, the resulting graph does not depend on the random choices, in the sense that it is almost surely isomorphic to a fixed graph. While this notion makes sense in the general context of metric spaces, previous work has been restricted to sets in Banach spaces. We study the case when the underlying metric space is a circle of circumference L, and find a surprising dependency of behaviour on the rationality of L.",
keywords = "Geometric random graphs, Graph isomorphism, Rado graph",
author = "Omer Angel and Yinon Spinka",
note = "Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG.",
year = "2021",
doi = "https://doi.org/10.1007/978-3-030-85325-9_2",
language = "الإنجليزيّة",
series = "Progress in Probability",
pages = "23--41",
booktitle = "Progress in Probability",
}