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Proof of the Hamiltonicity-Trace Conjecture for Singularly Perturbed Markov Chains

Published online by Cambridge University Press:  14 July 2016

Vladimir Ejov*
Affiliation:
University of South Australia
Nelly Litvak*
Affiliation:
University of Twente
Giang T. Nguyen*
Affiliation:
University of South Australia
Peter G. Taylor*
Affiliation:
University of Melbourne
*
Postal address: School of Mathematics and Statistics, University of South Australia, Mawson Lakes campus, Mawson Lakes SA 5095, Australia. Email address: [email protected]
∗∗ Postal address: Faculty of Electrical Engineering, Mathematics and Computer Science, Department of Applied Mathematics, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands. Email address: [email protected]
∗∗∗ Current address: Département d'informatique, Université Libre de Bruxelles, CP 212, Boulevard du Triomphe, 2, B-1050 Bruxelles, Belgium. Email address: [email protected]
∗∗∗∗ Postal address: Department of Mathematics and Statistics, University of Melbourne, Parkville VIC 3010, Australia. Email address: [email protected]
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Abstract

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We prove the conjecture formulated in Litvak and Ejov (2009), namely, that the trace of the fundamental matrix of a singularly perturbed Markov chain that corresponds to a stochastic policy feasible for a given graph is minimised at policies corresponding to Hamiltonian cycles.

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 2011 

References

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