  We consider several aspects of the scaling limit of percolation on random
planar triangulations, both finite and infinite. The equivalents for random
maps of Cardy's formula for the limit under scaling of various crossing
probabilities are given. The limit probabilities are expressed in terms of
simple events regarding Airy-Levy processes. Some explicit formulas for limit
probabilities follow from this relation by applying known results on stable
processes. Conversely, natural symmetries of the random maps imply identities
concerning the Airy-Levy processes.
