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The asymptotic shape of the branching random walk – CORRIGENDUM

Published online by Cambridge University Press:  16 October 2025

J. D. Biggins
J. D. Biggins*
Affiliation:
University of Sheffield (Retired)
*
*Postal address: Hicks Building, School of Mathematical and Physical Sciences, University of Sheffield, Hounsfield Road, Sheffield, S3 7RH. Email: j.biggins@sheffield.ac.uk
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Information

Type
Corrigendum
Information
Advances in Applied Probability , Volume 58 , Issue 1 , March 2026 , pp. 473
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Applied Probability Trust

The argument presented just after Equation (3.4) in this paper contains a consequential error that undermines the approach taken to the upper bound on the shape. The author acknowledged the error and provided a correct approach to the upper bound in [Reference Biggins2] and had used a correct argument earlier, in [Reference Biggins1]. Relevant results are also given in [Reference Biggins3, Section 4.2].

References

Biggins, J. D. (1976). Asymptotic properties of the branching random walk. D. Phil. Thesis; University of Oxford.Google Scholar
Biggins, J. D. (1980). Spatial spread in branching processes. In Biological Growth and Spread: Mathematical Theories and Applications. (Eds. W. Jäger, H. Rost, P. Tautu). Springer Berlin, Heidelberg. 57–67.Google Scholar
Biggins, J. D. (1997). How fast does a general branching random walk spread?. In Classical and Modern Branching Processes. (Eds. K. B. Athreya, P. Jagers). Springer New York, NY. 19–39.CrossRefGoogle Scholar