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In this work we study bond percolation on random causal triangulations. While in the sub-critical regime there is no phase transition, we show that for percolation on critical random causal triangulations there exists a non-trivial phase transition and we compute an upper bound for the critical probability. Furthermore, the critical value is shown to be almost surely constant. MSC 2010 subject classifications: Primary 60K35, 60K35; secondary 60K35doi:10.1214/16-bjps310 fatcat:5zh3uohubjaspchs4u2z62pc6m