Branching processes with lattice spatial dynamics and a finite set of particle generation centers (Q1930824)

The authors consider the simplest model of a branching random walk on \(\mathbb{Z}^d\) with continuous time, one type of particles and without extinction in which the reproduction of only one descendant is possible. If the rate of branching is determined by a nonnegative function \(\beta V(x)\), \(x\in \mathbb{Z}^d\), a correspondence between such branching random walks and the theory of phase transition for homopolymers is established [\textit{M. Cranston} et al., J. Funct. Anal. 256, No. 8, 2656--2696 (2009; Zbl 1162.82031)]. Some results that are similar to the results obtained in [loc cit.], but with substantially different proofs, are presented.