Rollo Davidson (b. Bristol, 8 October 1944, d. Piz Bernina, 29 July 1970) was a probabilist, alpinist, and Fellow-elect of Churchill College, Cambridge, who died aged 25 on Piz Bernina. He is known for his work on semigroups, stochastic geometry, and stochastic analysis, and for the Rollo Davidson Prize, given in his name to young probabilists.
At the time of Rollo's birth, Davidson's parents lived in The Chantry, Thornbury, Gloucestershire. His mother was Priscilla (née Chilver); his father, Brian Davidson, won a prize at Oxford for his study of classics, was president of the Oxford Union, and worked as a solicitor before becoming an executive with the Bristol Aeroplane Company. Rollo Davidson attended Winchester College before studying mathematics at Trinity College, Cambridge, from 1962 and becoming a research fellow there in 1967. He completed his PhD in 1968, under the supervision of David George Kendall. He continued at Cambridge as assistant lecturer, lecturer, and in 1970 fellow-elect. He died in a mountain climbing accident in 1970.
In stochastic geometry, Davidson is known for introducing the study of line processes, which he modelled as point processes on spaces of parameters of lines. The second winner of the Rollo Davidson Prize, Olav Kallenberg, won the prize for settling (negatively) a conjecture on line processes posed by Davidson in his thesis.
In stochastic analysis, also, Davidson has been described as a "remarkably original mathematician" who left a legacy of "tantalising unsolved problems". He particularly studied Delphic semigroups, a class of topological semigroups introduced by his advisor to study renewal sequences; Ruzsa & Székely (1988) write that, despite the many applications of these semigroups, Davidson was "the only one to contribute seriously to Delphic theory" after Kendall, and that "his untimely death certainly deprived this theory of interesting developments".
In 1975 a fund was established at Churchill College in his memory, endowed initially through the publication in his honour of two volumes of papers, edited by E. F. Harding and D. G. Kendall. A prize from the Rollo Davidson Trust Fund has been awarded annually since 1976 to young probabilists.
- Rollo Davidson: 1944–1970. Reprinted from Kendall & Harding (1973) pp. 449–452 and Harding & Kendall (1974) pp. 381–384.
- The Chantry: The Later History, Thornbury Roots. Retrieved 26 March 2015.
- Rollo Davidson at the Mathematics Genealogy Project
- Ripley, B. D. (1976), "The foundations of stochastic geometry", The Annals of Probability, 4 (6): 995–998, doi:10.1214/aop/1176995942, JSTOR 2242958, MR 0474454.
- Kallenberg, Olav (1977), "A counterexample to R. Davidson's conjecture on line processes", Mathematical Proceedings of the Cambridge Philosophical Society, 82 (2): 301–307, doi:10.1017/S0305004100053949, MR 0451399.
- Kingman, J. F. C. (2004), "Extremal problems for regenerative phenomena", Stochastic methods and their applications, Journal of Applied Probability, 41A: 333–346, doi:10.1239/jap/1082552209, JSTOR 3215987, MR 2057584.
- Kendall, David G. (1967), "Delphic semigroups", Bulletin of the American Mathematical Society, 73: 120–121, doi:10.1090/S0002-9904-1967-11673-2, MR 0203767.
- Ruzsa, Imre Z.; Székely, Gábor J. (1988), Algebraic probability theory, Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics, Chichester: John Wiley & Sons, Ltd., p. 61, ISBN 0-471-91803-2, MR 0974112.
- Kendall & Harding (1973); Harding & Kendall (1974)
- Rollo Davidson Trust
- Rollo Davidson Awards
- Kendall, D. G.; Harding, E. F. (1973), Stochastic Analysis: A tribute to the memory of Rollo Davidson, Wiley Series in Probability and Mathematical Statistics, London-New York-Sydney: John Wiley & Sons, MR 0350791.
- Harding, E. F.; Kendall, D. G. (1974), Stochastic Geometry: A tribute to the memory of Rollo Davidson, Wiley Series in Probability and Mathematical Statistics, London-New York-Sydney: John Wiley & Sons, MR 0350792.