Journal of Applied Probability

Proof of the Hamiltonicity-trace conjecture for singularly perturbed Markov chains

Vladimir Ejov, Nelly Litvak, Giang T. Nguyen, and Peter G. Taylor

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Abstract

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.

Article information

Source
J. Appl. Probab., Volume 48, Number 4 (2011), 901-910.

Dates
First available in Project Euclid: 16 December 2011

Permanent link to this document
https://projecteuclid.org/euclid.jap/1324046008

Digital Object Identifier
doi:10.1239/jap/1324046008

Mathematical Reviews number (MathSciNet)
MR2896657

Zentralblatt MATH identifier
1242.60076

Subjects
Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Secondary: 05C45: Eulerian and Hamiltonian graphs 11C20: Matrices, determinants [See also 15B36]

Keywords
Stochastic matrix Hamiltonian cycle perturbed Markov chain

Citation

Ejov, Vladimir; Litvak, Nelly; Nguyen, Giang T.; Taylor, Peter G. Proof of the Hamiltonicity-trace conjecture for singularly perturbed Markov chains. J. Appl. Probab. 48 (2011), no. 4, 901--910. doi:10.1239/jap/1324046008. https://projecteuclid.org/euclid.jap/1324046008


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