We study the random connection model on hyperbolic space Hᵈ in dimension d=2, 3. Vertices of the spatial random graph are given as a Poisson point process with intensity >0. Upon variation of there is a percolation phase transition: there exists a critical value c>0 such that for c. We identify certain critical exponents that characterize the clusters at (and near) c, and show that they agree with the mean-field values for percolation. We derive the exponents through isoperimetric properties of critical percolation clusters rather than via a calculation of the triangle diagram.
Dickson et al. (Tue,) studied this question.