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Here we prove critical exponents for Random Connections Models (RCMs) withinhomogeneous random marks. The vertices are given by a marked Poisson pointprocess on $\mathbb{R}^d$ and an edge exists between any pair of verticesindependently with a probability depending upon their spatial displacement andon their respective marks. Given conditions on the edge probabilities, we provemean-field lower bounds for the susceptibility and percolation functions. Inparticular, we prove the equality of the susceptibility and percolationcritical intensities. If we assume that a form of the triangle condition holds,then we also prove that the susceptibility, percolation and cluster tailcritical exponents exist and take their mean-field values. Our proof approachadapts the differential inequality and magnetization function approaches thathave been previously applied to discrete homogeneous settings to our continuuminhomogeneous setting. This includes a proof of the analyticity of themagnetization function in the required parameter regime.

Critical Exponents for Marked Random Connection Models