Mean‐field behaviour of the random connection model on hyperbolic space

We study the random connection model on hyperbolic space in dimension . Vertices of the spatial random graph are given as a Poisson point process with intensity . Upon variation of , there is a percolation phase transition: there exists a critical value such that for , all clusters are finite, but infinite clusters exist for . We identify certain critical exponents that characterise the clusters at (and near) , 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.