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Regular version of the site

Article

Zero-one law for random subgraphs of some distance graphs with vertices in Z^n

Sbornik Mathematics. 2016. Vol. 207. No. 3. P. 458-478.

The zero-one law for the model of random distance graphs with vertices in 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.