On the Mixing Time of Geographical Threshold Graphs
Published in Discrete Mathematics, 2011
A. Beveridge and M. Bradonjić, On the Mixing Time of Geographical Threshold Graphs, Discrete Mathematics, Vol. 311, No. 23-24 (2011), p. 2637-2649.
Preprint link: https://arxiv.org/abs/1109.4311
We study the mixing time of random graphs in the $d$-dimensional toric unit cube generated by the geographical threshold graph (GTG) model, a generalization of random geometric graphs (RGG). If the weight distribution function decays with $P[W≥x]=O(x^{-d+\nu})$ for an arbitrarily small $\nu >0$ then the mixing time of GTG is at least as fast as that of the corresponding random geometric graph (RGG).