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We consider discrete-time branching random walks with a radially symmetricdistribution. Independently of each other individuals generate offspring whoserelative locations are given by a copy of a radially symmetric point process$\mathcal{L}$. The number of particles at time $t$ form a supercriticalGalton-Watson process. We investigate the maximal distance to the origin ofsuch branching random walks. Conditioned on survival, we show that, under someassumptions on $\mathcal{L}$, it grows in the same way as for branchingBrownian motion or a broad class of one-dimensional branching random walks: thefirst term is linear in time and the second logarithmic. The constants in frontof these terms are explicit and depend only on the mean measure of$\mathcal{L}$ and dimension. Our main tool in the proof is a ballot theoremwith moving barrier which may be of independent interest.

The maximal displacement of radially symmetric branching random walk in $\mathbb{R}^d$