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We answer some questions on the asymptotics of ballot walks raised in[Personal Journal Shalosh B Ekhad and Doron Zeilberger, Apr 5, 2021; see alsoarXiv:2104.01731] and prove that these models are not D-finite. This short notedemonstrates how the powerful tools developed in the last decades on latticepaths in convex cones help us to answer some challenging problems that were outof reach for a long time. On the way we generalize tandem walks to the familyof large tandem walks whose steps are of arbitrary length and map thembijectively to a generalization of ballot walks in three dimensions.

On the critical exponents of generalized ballot sequences in three dimensions and large tandem walks