The asymptotic shape of the branching random walk
- 1 March 1978
- journal article
- research article
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 10 (01) , 62-84
- https://doi.org/10.1017/s0001867800029487
Abstract
In a supercritical branching random walk on R p , a Galton–Watson process with the additional feature that people have positions, let be the set of positions of the nth-generation people, scaled by the factor n –1. It is shown that when the process survives looks like a convex set for large n. An analogous result is established for an age-dependent branching process in which people also have positions. In certain cases an explicit formula for the asymptotic shape is given.Keywords
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