On transition matrices of Markov chains corresponding to Hamiltonian cycles - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Annals of Operations Research Year : 2016

On transition matrices of Markov chains corresponding to Hamiltonian cycles

Abstract

In this paper, we present some algebraic properties of a particular class of probability transition matrices, namely, Hamiltonian transition matrices. Each matrix P in this class corresponds to a Hamiltonian cycle in a given graph G on n nodes and to an irreducible, periodic, Markov chain. We show that a number of important matrices traditionally associated with Markov chains, namely, the stationary, fundamental, deviation and the hitting time matrix all have elegant expansions in the first n−1 powers of P , whose coefficients can be explicitly derived. We also consider the resolvent-like matrices associated with any given Hamiltonian cycle and its reverse cycle and prove an identity about the product of these matrices.
Fichier principal
Vignette du fichier
HamMatrixRev1.pdf (320.8 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-01402827 , version 1 (25-11-2016)

Identifiers

Cite

Konstantin Avrachenkov, Ali Eshragh, Jerzy A. Filar. On transition matrices of Markov chains corresponding to Hamiltonian cycles. Annals of Operations Research, 2016, 243 (1-2), pp.19 - 35. ⟨10.1007/s10479-014-1642-2⟩. ⟨hal-01402827⟩

Collections

INRIA INRIA2
241 View
547 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More