Book contents
- Frontmatter
- Contents
- The asymptotic speed and shape of a particle system
- On doubly stochastic population processes
- On limit theorems for occupation times
- The Martin boundary of two dimensional Ornstein-Uhlenbeck processes
- Green's and Dirichlet spaces for a symmetric Markov transition function
- On a theorem of Kabanov, Liptser and Širjaev
- Oxford Commemoration Ball
- Invariant measures and the q-matrix
- The appearance of a multivariate exponential distribution in sojourn times for birth-death and diffusion processes
- Three unsolved problems in discrete Markov theory
- The electrostatic capacity of an ellipsoid
- Stationary one-dimensional Markov random fields with a continuous state space
- A uniform central limit theorem for partial-sum processes indexed by sets
- Multidimensional randomness
- Some properties of a test for multimodality based on kernel density estimates
- Criteria for rates of convergence of Markov chains, with application to queueing and storage theory
- Competition and bottle-necks
- Contributors
Oxford Commemoration Ball
Published online by Cambridge University Press: 05 April 2013
- Frontmatter
- Contents
- The asymptotic speed and shape of a particle system
- On doubly stochastic population processes
- On limit theorems for occupation times
- The Martin boundary of two dimensional Ornstein-Uhlenbeck processes
- Green's and Dirichlet spaces for a symmetric Markov transition function
- On a theorem of Kabanov, Liptser and Širjaev
- Oxford Commemoration Ball
- Invariant measures and the q-matrix
- The appearance of a multivariate exponential distribution in sojourn times for birth-death and diffusion processes
- Three unsolved problems in discrete Markov theory
- The electrostatic capacity of an ellipsoid
- Stationary one-dimensional Markov random fields with a continuous state space
- A uniform central limit theorem for partial-sum processes indexed by sets
- Multidimensional randomness
- Some properties of a test for multimodality based on kernel density estimates
- Criteria for rates of convergence of Markov chains, with application to queueing and storage theory
- Competition and bottle-necks
- Contributors
Summary
Question for a demy
I hope this salute to my old friend David Kendall will remind him of his Oxford days, for it commemorates an excellent scholarship question that he once set in the 1950s when he was the mathematics tutor at Magdalen. The gist of the question ran as follows. A spherical ball of unit radius rests on an infinite horizontal table. You may imagine that it is a globe with a map of the world painted on its surface to distinguish its spatial orientations. The state of the ball is specified by specifying both its spatial orientation and its position on the table. You have to transfer the ball from a given initial state to an arbitrary final state via a sequence of moves. Each move consists of rolling the ball along some straight line on the table: the length and direction of any move are at your disposal, but the rolling must be pure in the sense that the axis of rotation must be horizontal and there must be no slipping between ball and table. How many moves, N, will be necessary and sufficient to reach any final state?
The original version of the question, set for 18–year–old schoolboys, invited candidates to investigate how two moves, each of length π, would change the ball's orientation; and to deduce in the first place that N ≤ 11, and in the second place that N ≤ 7. Candidates scored bonus marks for any improvement on 7 moves.
- Type
- Chapter
- Information
- Probability, Statistics and Analysis , pp. 112 - 142Publisher: Cambridge University PressPrint publication year: 1983
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