### Individuals at the origin in the critical catalytic branching random walk

*Valentin Topchii, Vladimir Vatutin*

#### Abstract

A continuous time branching random walk on the lattice

**Z**is considered in which individuals may produce children at the origin only. Assuming that the underlying random walk is symmetric and the offspring reproduction law is critical we prove a conditional limit theorem for the number of individuals at the origin.Full Text: GZIP Compressed PostScript PostScript PDF original HTML abstract page