Critical periodic branching random walk on $\mathbf {Z}^d$ with immigration

I. I. Lukashova<sup>ab

a</sup> St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences
^b Euler International Mathematical Institute, St. Petersburg

Abstract: We consider a continuous-time branching random walk with immigra-tion on $\mathbf {Z}^d$ with branching sources located periodically. The asymptotic behavior of the mean number of particles at an arbitrary point is obtained for $t\to\infty$ in the critical case.

Key words and phrases: branching random walk, periodic perturbation, the direct integral decomposition, critical case.

UDC: 519.2

Received: 14.10.2025