The Genealogy of Genealogy Branching Processes before (and after) 1873
Bulletin of the London Mathematical Society, 7 (3):
225-253 (1975)DOI: 10.1112/blms/7.3.225
Abstract
Branching-process theory, the reader may like to be reminded, is that part of
mathematics which deals with the growth and decay of populations of objects which
multiply and replace one another, generation by generation, according to rules in
which chance plays a prominent part. In the earliest work these objects were always
human males, and interest was focussed on the rate of diminution of the stock of
family names (' surnames'). In contemporary applications the objects might be
heterozygotes carrying a mutant gene, customers waiting in a queueing system, or
neutrons in a nuclear reactor, to mention only three of the more important examples.
For further details, see 1.
Nearly ten years ago, on the occasion of the centenary of the London Mathematical
Society, I gave a lecture 15 on the history of the theory of branching processes
' since 1873 ' (its then supposed date of origin). This now calls for substantial sup-
plementation, both as regards the later history (especially of the Russian contribu-
tions), and also as regards the earlier history, the very existence of which was alto-
gether unsuspected until its discovery in 1972 by C. C. Heyde and E. Seneta 13.