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We investigate a spatial random graph model whose vertices are given as amarked Poisson process on $\mathbb{R}^d$. Edges are inserted between any pairof points independently with probability depending on the spatial displacementof the two endpoints and on their marks. Upon variation of the Poisson density,a percolation phase transition occurs under mild conditions: for low densitythere are finite connected components only, whilst for large density there isan infinite component almost surely. Our focus is on the transition between thelow- and high-density phase, where the system is critical. We prove that if thedimension is high enough and the edge probability function satisfies certainconditions, then an infrared bound for the critical connection function isvalid. This implies the triangle condition, thus indicating mean-fieldbehaviour. We achieve this result through combining the recently establishedlace expansion for Poisson processes with spectral estimates.

The Triangle Condition for the Marked Random Connection Model