Fluctuation Theory for the Ehrenfest urn
- 1 June 1991
- journal article
- research article
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 23 (03), 598-611
- https://doi.org/10.1017/s0001867800023752
Abstract
The Ehrenfest urn model withdballs, or alternatively random walk on the unit cube inddimensions, is considered in discrete and continuous time, together with related models. Attention is focused on the fluctuation theory of the model—behaviour on unusual states—and in particular on first passage to the opposite vertex. Applications to statistical mechanics, reliability theory and genetics are surveyed, and some new results are obtained.Keywords
This publication has 29 references indexed in Scilit:
- Brownian motion on the Sierpinski gasketProbability Theory and Related Fields, 1988
- Shuffling Cards and Stopping TimesThe American Mathematical Monthly, 1986
- Exponential trends of Ornstein–Uhlenbeck first-passage-time densitiesJournal of Applied Probability, 1985
- Minimization Algorithms and Random Walk on the $d$-CubeThe Annals of Probability, 1983
- Les fonctions sphériques d'un couple de Gelfand symétrique et les chaînes de MarkovAdvances in Applied Probability, 1982
- Markov FunctionsThe Annals of Probability, 1981
- Random walks on a dodecahedronJournal of Applied Probability, 1980
- Random Walks on A 600-CellSIAM Journal on Algebraic Discrete Methods, 1980
- On exponential ergodicity and spectral structure for birth-death processes IStochastic Processes and their Applications, 1973
- Recurrence times for the Ehrenfest modelPacific Journal of Mathematics, 1951