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

Vladimir Ejov; Nelly Litvak; Giang Nguyen; Peter Taylor

doi:10.1239/jap/1324046008

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

Vladimir Ejov, Nelly Litvak, Giang Nguyen, Peter Taylor

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

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.

Original language	English
Pages (from-to)	901-910
Number of pages	10
Journal	JOURNAL OF APPLIED PROBABILITY
Volume	48
Issue number	4
DOIs	https://doi.org/10.1239/jap/1324046008
Publication status	Published - Dec 2011

Keywords

Hamiltonian cycle
Perturbed Markov chain
Stochastic matrix

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10.1239/jap/1324046008

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title = "Proof of the Hamiltonicity-trace conjecture for singularly perturbed Markov chains",

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.",

keywords = "Hamiltonian cycle, Perturbed Markov chain, Stochastic matrix",

author = "Vladimir Ejov and Nelly Litvak and Giang Nguyen and Peter Taylor",

year = "2011",

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AU - Ejov, Vladimir

AU - Litvak, Nelly

AU - Nguyen, Giang

AU - Taylor, Peter

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AB - 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.

KW - Hamiltonian cycle

KW - Perturbed Markov chain

KW - Stochastic matrix

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M3 - Article

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JO - JOURNAL OF APPLIED PROBABILITY

JF - JOURNAL OF APPLIED PROBABILITY

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IS - 4

ER -

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

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Keywords

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