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On a Branching Annihilating Random Walk We consider a discrete-time branching annihilating random walk (BARW). Within a time step, each particle, before dying, produces a random number of offspring which are then randomly and independently displaced in space. If, after the displacement, a site is occupied by several particles, all particles at that site are annihilated. This can be thought of as a very strong form of local competition and entails that the system is not monotone. The motivation of our current discussion stems from the long-term behaviour of this model on Z^d. For a Poissonian number of offspring and a uniform displacement within a ball of finite radius around the parent’s position, survival and complete convergence results were shown by Birkner et al. (2024). While a survival result was obtained for a more general class of offspring distributions, the extension of the complete convergence result to general offspring laws has proven to be more intricate. To gain more insight on this process, we further investigate the mean-field version of the BARW with general offspring law. In this talk, we will thus explore the BARW on the complete graph and highlight its connection to a deterministic dynamical system as well as a classical urn occupancy problem. We then discuss a local central limit result on the related urn occupancy problem based on Stein’s method. This result enables us to construct couplings, which potentially lay the foundation to prove the complete convergence result for the spatial model.