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Fluctuation theory for 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:
New Jersey Institute of Technology
*
∗Postal address: Department of Mathematics, New Jersey Institute of Technology, Newark, NJ 07102, USA.
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Abstract

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Using the electric network approach, we give very simple derivations for the expected first passage from the origin to the opposite vertex in the d-cube (i.e. the Ehrenfest urn model) and the Platonic graphs.

Keywords

FIRST PASSAGEEFFECTIVE RESISTANCE

MSC classification

Primary: 60C05: Combinatorial probability
Type
Letters to the Editor
Information
Advances in Applied Probability , Volume 25 , Issue 2 , June 1993 , pp. 472 - 476
Copyright
Copyright © Applied Probability Trust 1993 

References

Baróti, G. (1988) First passage problems for Ehrenfest model. In Prob. Theo. Math. Stat. Appl.: Proc. 5th Pannonian Symp. Math. Stat. , Visegrád, Hungary 1985, pp. 3–6, Reidel, Boston, MA.Google Scholar
Bingham, N. H. (1991) Fluctuation theory for the Ehrenfest urn. Adv. Appl. Prob. 23, 598–611.CrossRefGoogle 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 Proc. 21st Annual ACM Symp. on Theory of Computing , Seattle, Washington, pp. 574–586.Google Scholar
Doyle, P. G. and Snell, J. L. (1984) Random Walks and Electrical Networks. Mathematical Association of America, Washington, DC.CrossRefGoogle Scholar
Kac, M. (1959) Probability and Related Topics in Physical Sciences. Interscience, London.Google Scholar
Karlin, S. and Mcgregor, J. (1965) Ehrenfest urn models. J. Appl. Prob. 2, 352–376.CrossRefGoogle Scholar
Kemeny, J. G., Snell, J. L. and Knapp, A. W. (1966) Denumerable Markov Chains. Van Nostrand, Princeton, NJ.Google Scholar
Matthews, P. (1989) Some sample-path properties of a random walk on the cube. J. Theoret. Prob. 2, 129–157.CrossRefGoogle Scholar
Palacios, J. L. (1992) Expected hitting and cover times of random walks on some special graphs. Proc. 'Random Graphs ‘91’ , Poznan, Poland.Google Scholar