John F. C. Kingman

University of Cambridge

Election Year: 2007
Primary Section: 32, Applied Mathematical Sciences
Secondary Section: 11, Mathematics
Membership Type: Foreign Associate

Research Interests

I work on the mathematical theory of probability, and on some of its many applications. My purely theoretical work lies largely in Markov processes and Poisson processes. I developed the theory of regenerative phenomena, partly to settle a difficult question of Kolmogorov on characterizing Markov transition probabilities. Although this theory is now mature, there are hard unsolved problems, for instance in limiting the possible oscillations of probabilities with time. I also work on sub additive processes, which have found many applications since I proved the ergodic theorem conjectured by Hammersley and Welsh. Among the applied areas of my interest is the analysis of queuing systems, which has recently become more active because for instance of congestion on the internet. I also work on mathematical problems in population genetics, seeking to clarify the biological explanations of genetic diversity. The simple concept of the coalescent, which describes the family tree of a group of individuals run backwards in time, has proved an effective approach to some of these problems.

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