Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-12-03T19:18:58.132Z Has data issue: false hasContentIssue false
  • English
  • Français

Another Look at the Ehrenfest Urn Via Electric Networks

Part of: Combinatorial probability

Published online by Cambridge University Press:  01 July 2016

José Luis Palacios
José Luis Palacios*
Affiliation:
Universidad Simón Bolívar
*
* Postal address: Universidad Simón Bolívar, Departamento de Matemáticas, Apartado 89,000, Caracas, Venezuela.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Using the electric network approach, we give closed-form formulas for the expected hitting times in the Ehrenfest urn model.

Keywords

FIRST PASSAGEEFFECTIVE RESISTANCE

MSC classification

Primary: 60C05: Combinatorial probability
Type
Letters to the Editor
Information
Advances in Applied Probability , Volume 26 , Issue 3 , September 1994 , pp. 820 - 824
Copyright
Copyright © Applied Probability Trust 1994 

Footnotes

Part of this work was done while the author was with the New Jersey Institute of Technology.

References

Aldous, D. J. (1982) Some inequalities for reversible Markov chains. J. London Math. Soc. 25, 564–576.CrossRefGoogle Scholar
Aldous, D. J. (1983) Random walks on finite groups and rapidly mixing Markov chains. In Lecture Notes in Mathematics 986, pp. 243–297. Springer-Verlag, Berlin.Google Scholar
Bingham, N. H. (1991) Fluctuation theory for the Ehrenfest urn. Adv. Appl. Prob. 23, 598–611.Google Scholar
Blom, G. (1989) Mean transition times for the Ehrenfest urn model. Adv. Appl. Prob. 21, 479–480.Google Scholar
Chandra, A. K., Raghavan, P., Ruzzo, W. L., Smolensky, R. and Tiwari, P. (1989) The electrical resistance of a graph captures its commute and cover times. In Proceedings of the 21st Annual ACM Symposium on Theory of Computing, Seattle, Washington, pp. 547–586.Google Scholar
Doyle, P. G. and Snell, J. L. (1984) Random Walks and Electrical Networks. Mathematical Association of America, Washington, DC.CrossRefGoogle Scholar
Karlin, S. and Mcgregor, J. (1965) Ehrenfest urn models. J. Appl. Prob. 2, 352–376.CrossRefGoogle Scholar
Kemperman, J. H. B. (1961) The Passage Problem for a Stationary Markov Chain. University of Chicago Press.Google Scholar
Palacios, J. L. (1992) Expected cover times of random walks on symmetric graphs. J. Theoret. Prob. 5, 597–600.Google Scholar
Palacios, J. L. (1993) Fluctuation theory for the Ehrenfest urn via electric networks. Adv. Appl. Prob. 25, 472–476.Google Scholar
Stanton, D. (1984) Orthogonal polynomials and Chevalley groups. In Special Functions: Group Theoretical Aspects and Applications. pp. 87–128. Reidel, Dordrecht.Google Scholar
Tetali, P. (1991) Random walks and the effective resistance of networks. J. Theoret. Prob. 4, 101–109.Google Scholar