Survival of nearest-particle systems with low birth rate
Nearest particle systems on \({\mathbb{Z}}\) are constructed, for which the probability rates of birth of a particle between two nearest particles are \(1+\epsilon\) whereas the death rate of any particle is 1, and the system survives for all times. The proof is based on the comparison with a contact discrete-time process studied formerly by \textit{R. Durrett} [ibid. 12, 999-1040 (1984; Zbl 0567.60095)].
scientific article; zbMATH DE number 4117621