Rollo Davidson

Last updated

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, [1] and for the Rollo Davidson Prize, given in his name to early-career probabilists.

Contents

Life

At the time of Davidson's birth, his 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. [2] Rollo Davidson attended Winchester College before studying mathematics at Trinity College, Cambridge, from 1962 and becoming a research fellow there in 1967. [1] He completed his PhD in 1968, under the supervision of David George Kendall. [3] He continued at Cambridge as assistant lecturer, lecturer, and in 1970 fellow-elect. He died in a mountain climbing accident in 1970. [1]

Contributions

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. [4] 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. [5]

In stochastic analysis, also, Davidson has been described as a "remarkably original mathematician" who left a legacy of "tantalising unsolved problems". [6] He particularly studied Delphic semigroups, a class of topological semigroups introduced by his advisor to study renewal sequences; [7] 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". [8]

Legacy

In 1975 a fund was established at Churchill College in his memory, endowed initially through the publication in his honour of two volumes [9] of papers, edited by E. F. Harding and D. G. Kendall. [10] A prize from the Rollo Davidson Trust Fund has been awarded annually since 1976 to early-career probabilists. [11]

See also

Related Research Articles

<span class="mw-page-title-main">Stochastic process</span> Collection of random variables

In probability theory and related fields, a stochastic or random process is a mathematical object usually defined as a sequence of random variables in a probability space, where the index of the sequence often has the interpretation of time. Stochastic processes are widely used as mathematical models of systems and phenomena that appear to vary in a random manner. Examples include the growth of a bacterial population, an electrical current fluctuating due to thermal noise, or the movement of a gas molecule. Stochastic processes have applications in many disciplines such as biology, chemistry, ecology, neuroscience, physics, image processing, signal processing, control theory, information theory, computer science, and telecommunications. Furthermore, seemingly random changes in financial markets have motivated the extensive use of stochastic processes in finance.

William "Vilim" Feller, born Vilibald Srećko Feller, was a Croatian–American mathematician specializing in probability theory.

<span class="mw-page-title-main">Piz Bernina</span> Highest mountain in the Eastern Alps

Piz Bernina is the highest mountain in the Eastern Alps, the highest point of the Bernina Range, and the highest peak in the Rhaetian Alps. It rises 4,048 m (13,281 ft) and is located south of Pontresina in the Bernina Region and near the major Alpine resort of St. Moritz, in the Engadin valley. It is also the most easterly mountain higher than 4,000 m (13,000 ft) in the Alps, the highest point of the Swiss canton of Grisons, and the fifth-most prominent peak in the Alps. Although the summit lies within Switzerland, the massif is on the border with Italy. The "shoulder" known as La Spedla is the highest point in the Italian Lombardy region.

<span class="mw-page-title-main">Olav Kallenberg</span> Swedish American mathematician

Olav Kallenberg is a probability theorist known for his work on exchangeable stochastic processes and for his graduate-level textbooks and monographs. Kallenberg is a professor of mathematics at Auburn University in Alabama in the USA.

<span class="mw-page-title-main">Wendelin Werner</span>

Wendelin Werner is a German-born French mathematician working on random processes such as self-avoiding random walks, Brownian motion, Schramm–Loewner evolution, and related theories in probability theory and mathematical physics. In 2006, at the 25th International Congress of Mathematicians in Madrid, Spain he received the Fields Medal "for his contributions to the development of stochastic Loewner evolution, the geometry of two-dimensional Brownian motion, and conformal field theory". He is currently Rouse Ball professor of Mathematics at the University of Cambridge.

<span class="mw-page-title-main">Daniel W. Stroock</span> American mathematician

Daniel Wyler Stroock is an American mathematician, a probabilist. He is regarded and revered as one of the fundamental contributors to Malliavin calculus with Shigeo Kusuoka and the theory of diffusion processes with S. R. Srinivasa Varadhan with an orientation towards the refinement and further development of Itô’s stochastic calculus.

The Applied Probability Trust is a UK-based non-profit foundation for study and research in the mathematical sciences, founded in 1964 and based in the School of Mathematics and Statistics at the University of Sheffield, which it has been affiliated with since 1964.

<span class="mw-page-title-main">Peter Gavin Hall</span> Australian statistician (1951–2016)

Peter Gavin Hall was an Australian researcher in probability theory and mathematical statistics. The American Statistical Association described him as one of the most influential and prolific theoretical statisticians in the history of the field. The School of Mathematics and Statistics Building at The University of Melbourne was renamed the Peter Hall building in his honour on 9 December 2016.

<span class="mw-page-title-main">Institute of Mathematics of National Academy of Sciences of Armenia</span>

The Institute of Mathematics of National Academy of Sciences of Armenia is owned and operated by the Armenian Academy of Sciences, located in Yerevan.

<span class="mw-page-title-main">David Aldous</span> British-American mathematician

David John Aldous FRS is a mathematician known for his research on probability theory and its applications, in particular in topics such as exchangeability, weak convergence, Markov chain mixing times, the continuum random tree and stochastic coalescence. He entered St. John's College, Cambridge, in 1970 and received his Ph.D. at the University of Cambridge in 1977 under his advisor, D. J. H. Garling. Aldous was on the faculty at University of California, Berkeley from 1979 until his retirement in 2018.

The Rollo Davidson Prize is a prize awarded annually to early-career probabilists by the Rollo Davidson trustees. It is named after English mathematician Rollo Davidson (1944–1970).

<span class="mw-page-title-main">Geoffrey Grimmett</span> English mathematician (born 1950)

Geoffrey Richard GrimmettOLY is an English mathematician known for his work on the mathematics of random systems arising in probability theory and statistical mechanics, especially percolation theory and the contact process. He is the Professor of Mathematical Statistics in the Statistical Laboratory, University of Cambridge, and was the Master of Downing College, Cambridge, from 2013 to 2018.

<span class="mw-page-title-main">James R. Norris</span> British mathematician

James Ritchie Norris is a mathematician working in probability theory and stochastic analysis. He is the Professor of Stochastic Analysis in the Statistical Laboratory, University of Cambridge.

Gareth Owen Roberts FRS FLSW is a statistician and applied probabilist. He is Professor of Statistics in the Department of Statistics and Director of the Centre for Research in Statistical Methodology (CRiSM) at the University of Warwick. He is an established authority on the stability of Markov chains, especially applied to Markov chain Monte Carlo (MCMC) theory methodology for a wide range of latent statistical models with applications in spatial statistics, infectious disease epidemiology and finance.

John Charles Gittins is a researcher in applied probability and operations research, who is a professor and Emeritus Fellow at Keble College, Oxford University.

<span class="mw-page-title-main">Gábor J. Székely</span>

Gábor J. Székely is a Hungarian-American statistician/mathematician best known for introducing energy statistics (E-statistics). Examples include: the distance correlation, which is a bona fide dependence measure, equals zero exactly when the variables are independent; the distance skewness, which equals zero exactly when the probability distribution is diagonally symmetric; the E-statistic for normality test; and the E-statistic for clustering.

<span class="mw-page-title-main">Poisson point process</span> Type of random mathematical object

In probability theory, statistics and related fields, a Poisson point process is a type of mathematical object that consists of points randomly located on a mathematical space with the essential feature that the points occur independently of one another.. The process's name derives from the fact that the distribution of the number of points regions of the same size has a Poisson distribution. The process and the distribution are named after French mathematician Siméon Denis Poisson. The process itself was discovered independently and repeatedly in several settings, including experiments on radioactive decay, telephone call arrivals and actuarial science.

<span class="mw-page-title-main">Rouben V. Ambartzumian</span> Armenian mathematician

Rouben V. Ambartzumian is an Armenian mathematician and Academician of National Academy of Sciences of Armenia. He works in Stochastic Geometry and Integral Geometry where he created a new branch, combinatorial integral geometry. The subject of combinatorial integral geometry received support from mathematicians K. Krickeberg and D. G. Kendall at the 1976 Sevan Symposium (Armenia) which was sponsored by Royal Society of London and The London Mathematical Society. In the framework of the later theory he solved a number of classical problems in particular the solution to the Buffon Sylvester problem as well as Hilbert's fourth problem in 1976. He is a holder of the Rollo Davidson Prize of Cambridge University of 1982. Rouben's interest in Integral Geometry was inherited from his father. Nobel prize winner Allan McLeod Cormack Laureate for Tomography wrote: "Ambartsumian gave the first numerical inversion of the Radon transform and it gives the lie to the often made statement that computed tomography would have been impossible without computers". Victor Hambardzumyan, in his book "A Life in Astrophysics", wrote about the work of Rouben V. Ambartzumian, "More recently, it came to my knowledge that the invariance principle or invariant embedding was applied in a purely mathematical field of integral geometry where it gave birth to a novel, combinatorial branch." See R. V. Ambartzumian, «Combinatorial Integral Geometry», John Wiley, 1982.

<span class="mw-page-title-main">Laurent Saloff-Coste</span> French mathematician (born 1958)

Laurent Saloff-Coste is a French mathematician whose research is in Analysis, Probability theory, and Geometric group theory. He is a professor of mathematics at Cornell University.

Khinchin's theorem on the factorization of distributions says that every probability distribution P admits a factorization

References

  1. 1 2 3 Rollo Davidson: 1944–1970 Archived 18 February 2012 at the Wayback Machine . Reprinted from Kendall & Harding (1973) pp. 449–452 and Harding & Kendall (1974) pp. 381–384.
  2. The Chantry: The Later History, Thornbury Roots. Retrieved 26 March 2015.
  3. Rollo Davidson at the Mathematics Genealogy Project
  4. 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 .
  5. Kallenberg, Olav (1977), "A counterexample to R. Davidson's conjecture on line processes", Mathematical Proceedings of the Cambridge Philosophical Society, 82 (2): 301–307, Bibcode:1977MPCPS..82..301K, doi:10.1017/S0305004100053949, MR   0451399 .
  6. 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, S2CID   123576712 .
  7. 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 .
  8. 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 .
  9. Kendall & Harding (1973); Harding & Kendall (1974)
  10. Rollo Davidson Trust
  11. Rollo Davidson Awards 1976 - 2021

Further reading