  We study the mixing time of random graphs in the $d$-dimensional toric unit
cube $[0,1]^d$ generated by the geographical threshold graph (GTG) model, a
generalization of random geometric graphs (RGG). In a GTG, nodes are
distributed in a Euclidean space, and edges are assigned according to a
threshold function involving the distance between nodes as well as randomly
chosen node weights, drawn from some distribution. The connectivity threshold
for GTGs is comparable to that of RGGs, essentially corresponding to a
connectivity radius of $r=(\log n/n)^{1/d}$. However, the degree distributions
at this threshold are quite different: in an RGG the degrees are essentially
uniform, while RGGs have heterogeneous degrees that depend upon the weight
distribution. Herein, we study the mixing times of random walks on
$d$-dimensional GTGs near the connectivity threshold for $d \geq 2$. If the
weight distribution function decays with $\mathbb{P}[W \geq x] =
O(1/x^{d+\nu})$ for an arbitrarily small constant $\nu>0$ then the mixing time
of GTG is $\mixbound$. This matches the known mixing bounds for the
$d$-dimensional RGG.
