Geodesic
Individuals at the origin in the critical catalytic branching random walk
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AC, Discrete Random Walks (DRW'03), DMTCS Proceedings vol. AC, Discrete Random Walks (DRW'03) (2003).

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A continuous time branching random walk on the lattice $\mathbb{Z}$ 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. 
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     author = {Topchii, Valentin and Vatutin, Vladimir},
     title = {Individuals at the origin in the critical catalytic branching random walk},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AC, Discrete Random Walks (DRW'03)},
     year = {2003},
     doi = {10.46298/dmtcs.3331},
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     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3331/}
}
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Topchii, Valentin; Vatutin, Vladimir. Individuals at the origin in the critical catalytic branching random walk. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AC, Discrete Random Walks (DRW'03), DMTCS Proceedings vol. AC, Discrete Random Walks (DRW'03) (2003). doi : 10.46298/dmtcs.3331. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3331/

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