Probability at Durham

Some historical notes


Durham played a part in the expansion of probability theory in the UK in the 1950s and 1960s. Among the key players in this was GEH Reuter.

Reuter's background was in analysis, but from the early 1950s he began a sequence of seminal works on the theory of Markov processes.

Reuter joined Durham on 1 January 1959 as Professor of Pure Mathematics, and left in 1965 to join DR Cox's group at Imperial College, London. During this time Reuter became Head of Department in Durham (he was Chairman of the Board of Studies in Mathematics from 1963–1965, succeeded by TJ Willmore).

Reuter had already established his famous collaboration with DG Kendall: the two first met at the British Mathematical Colloquium held in Durham 8–10 September, 1953. [K86]

Computer scientist ES Page was appointed as director of Durham University's Computing Laboratory in 1957. The Computing Laboratory was located at King's College, Newcastle, until King's College became the University of Newcastle upon Tyne in 1963. Page worked in Newcastle until 1979, including serving as acting Vice-Chancellor from 1976. Page had research interests in probability, and is known for his 1959 contribution to Flory's model of discrete random parking, for example [P59].


In December 1961, Kendall and Reuter initiated the informal Stochastic Analysis Group with the aims

"(1) to create a home for probabilists, and (2) to create more effective contact between the London Mathematical Society and the Royal Statistical Society" [K95].

Related to this initiative, the London Mathematical Society (LMS) was persuaded to hold an Instructional Conference on Mathematical Probability in Durham from March 28 till April 11, 1963.

"This did much to interest pure mathematicians in the subject, and paved the way for a similar Conference on Algebraic Number Theory held in the University of Sussex in 1965, thus establishing what became a regular and valuable part of the LMS programme. The choice of Durham as a venue in 1963 was a natural consequence of the fact that Harry was by now Professor there, and ever since there has been a close association between that University and the LMS" [K95].

The conference had 153 participants, and included lectures by Kendall and Reuter, as well as P Billingsley, DA Edwards, M Kac, JFC Kingman, and SJ Taylor [C63].

The association between the LMS and Durham continued over many years via the LMS Durham Symposia, established in 1974.

Reuter supervised several PhD students in probability while at Durham, including RA Doney (Some problems on random walks, 1964) and CJ Ridler-Rowe (Some two-dimensional Markov processes, 1964), and, jointly with Kendall in Oxford, D Williams (Random time substitution in Markov chains, 1962).

Williams took up a lectureship in Durham from 1964–1966, after a year in Stanford (1962–1963) and before moving to Cambridge.

In 1964 the Applied Probability Trust was established by JM Gani with initial support garnered by Kendall from the LMS, under their President Dame Mary Cartwright and Treasurer Sir Edward Collingwood, who became one of the Trustees [G88]. Collingwood was Chairman of the Council of Durham University from 1955 till his death in 1970, and Durham's Collingwood College is named after him. He was knighted in 1962, elected to the Royal Society in 1965 and served as President of the LMS during 1969–1970.


AG Hawkes, who had been a student of MS Bartlett, was Reader in Mathematical Statistics in Durham from 1 January 1969 until 1975, succeeding the previous Reader, statistician M Stone. It was during this period that Hawkes introduced the point processes now known as Hawkes processes [H71].

While in Durham, Hawkes supervised PhD students including RJ Reed (Priority queues, 1971) and L Adamopoulos (Statistical analysis of earthquake data, 1973).

J Besag, another student of Bartlett, succeeded Hawkes as Reader in Mathematical Statistics from April 1975, and stayed in Durham until 1989 (as Professor since 1986). At Durham, Besag supervised S Zachary (Markov random fields on trees, 1981).

PJ Green, some of whose early work was in applied probability (including his PhD under DP Kennedy), was a lecturer in Durham from 1978–1989.


IM MacPhee joined the department as a Temporary Lecturer in 1987, and his position became permanent in 1990. He was promoted to Reader in 2010. While in Durham he supervised PhD students NH Antoniu (Optimal admission policies for small star networks, 1994), BP Jordan (On optimal search for a moving target, 1997), LJ Müller (Stability criteria for controlled queueing networks, 2006), and A Aboalkhair (Nonparametric predictive inference for system reliability, 2012, jointly supervised with FPA Coolen).


[B92] N.H. Bingham, Obituary: G. E. H. Reuter, Journal of Applied Probability 29 (1992) 754–757. JSTOR link.
[C63] Current Notes, Journal of the Royal Statistical Society. Series A. 126 (1963) 484–486. JSTOR link.
[G88] J. Gani, Adventures in applied probability, Journal of Applied Probability 25 A Celebration of Applied Probability (1988) 3–23. JSTOR link.
[H71] A.G. Hawkes, Spectra of some self-exciting and mutually exciting point processes. Biometrika 58 (1971) 83–90. Article link.
[K86] D.G. Kendall, Harry Reuter: An appreciation, Advances in Applied Probability 18 Analytic and Geometric Stochastics: Papers in Honour of G. E. H. Reuter (1986) 1–7. JSTOR link.
[K95] D.G. Kendall, Obituary: Gerd Edzard Harry Reuter, Bulletin of the London Mathematical Society 27 (1995) 177–188. Article link.
[K10] J.F.C. Kingman, A fragment of autobiography, 1957–1967, Probability and Mathematical Genetics: Papers in Honour of Sir John Kingman, London Mathematical Society Lecture Note Series 378, pp. 17–34, 2010.
[P59] E.S. Page, The distribution of vacancies on a line. J. Roy. Statist. Soc. Ser. B 21 (1959) 364–374. JSTOR link.
[DUC] Durham University Calendar, Vol I, Almanac and Lists.