Geodesic
Zero-one law for random subgraphs of some distance graphs with vertices in~$\mathbb Z^n$
Sbornik. Mathematics, Tome 207 (2016) no. 3, pp. 458-478

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The zero-one law for the model of random distance graphs with vertices in $\mathbb Z^n$ is studied. Sufficient conditions for a sequence of random distance graphs to obey the zero-one law are derived, as well as conditions under which it contains a subsequence obeying the zero-one law. Bibliography: 20 titles.
Keywords: random graphs, zero-one law, distance graphs. 
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     author = {S. N. Popova},
     title = {Zero-one law for random subgraphs of some distance graphs with vertices in~$\mathbb Z^n$},
     journal = {Sbornik. Mathematics},
     pages = {458--478},
     publisher = {mathdoc},
     volume = {207},
     number = {3},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2016_207_3_a7/}
}
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S. N. Popova. Zero-one law for random subgraphs of some distance graphs with vertices in~$\mathbb Z^n$. Sbornik. Mathematics, Tome 207 (2016) no. 3, pp. 458-478. http://geodesic.mathdoc.fr/item/SM_2016_207_3_a7/