Asymptotics of the Mean Number of Particles in a Periodic Branching Random Walk at a Receding Point

Branching random walks on the lattice Zᵈ are studied. The model under consideration includes the symmetric periodic random walks and periodic branchings. The main result is an asymptotic formula for the mean number of particles at a point receding from the origin as O(t^α) , where α∈[0,5/6) . Our findings extend the available results on front propagation in branching random walks.