Phase transition in random distance graphs on the torus
/ Authors
/ Abstract
We apply here methods of inhomogeneous random graphs to a class of random distance graphs. This provides an example outside of the rank 1 models which is still solvable as long as the largest connected component is concerned. In particular, we show that some random distance graphs behave exactly as the classical Erd\H{o}s-R\'enyi model not only in the supercritical phase (as was already known) but in the subcritical case as well.
Journal: J. Appl. Probab.
DOI: 10.1017/jpr.2017.63