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5 - Branching out

Published online by Cambridge University Press:  07 September 2011

J. D. Biggins
Affiliation:
University of Sheffield
N. H. Bingham
Affiliation:
Imperial College, London
C. M. Goldie
Affiliation:
University of Sussex
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Summary

Abstract

Results on the behaviour of the rightmost particle in the nth generation in the branching random walk are reviewed and the phenomenon of anomalous spreading speeds, noticed recently in related deterministic models, is considered. The relationship between such results and certain coupled reaction-diffusion equations is indicated.

AMS subject classification (MSC2010) 60J80

Introduction

I arrived at the University of Oxford in the autumn of 1973 for postgraduate study. My intention at that point was to work in Statistics. The first year of study was a mixture of taught courses and designated reading on three areas (Statistics, Probability, and Functional Analysis, in my case) in the ratio 2:1:1 and a dissertation on the main area. As part of the Probability component, I attended a graduate course that was an exposition, by its author, of the material in Hammersley (1974), which had grown out of his contribution to the discussion of John's invited paper on subadditive ergodic theory (Kingman, 1973). A key point of Hammersley's contribution was that the postulates used did not cover the time to the first birth in the nth generation in a Bellman–Harris process. Hammersley (1974) showed, among other things, that these quantities did indeed exhibit the anticipated limit behaviour in probability. I decided not to be examined on this course, which was I believe a wise decisin but I was intrigued by the material. That interest turned out to be critical a few months later.

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Probability and Mathematical Genetics
Papers in Honour of Sir John Kingman
, pp. 113 - 134
Publisher: Cambridge University Press
Print publication year: 2010

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  • Branching out
  • Edited by N. H. Bingham, Imperial College, London, C. M. Goldie, University of Sussex
  • Book: Probability and Mathematical Genetics
  • Online publication: 07 September 2011
  • Chapter DOI: https://doi.org/10.1017/CBO9781139107174.007
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  • Branching out
  • Edited by N. H. Bingham, Imperial College, London, C. M. Goldie, University of Sussex
  • Book: Probability and Mathematical Genetics
  • Online publication: 07 September 2011
  • Chapter DOI: https://doi.org/10.1017/CBO9781139107174.007
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Branching out
  • Edited by N. H. Bingham, Imperial College, London, C. M. Goldie, University of Sussex
  • Book: Probability and Mathematical Genetics
  • Online publication: 07 September 2011
  • Chapter DOI: https://doi.org/10.1017/CBO9781139107174.007
Available formats
×