Graduate School and Research Center In communication systems

Maximum entropy mixing time of circulant Markov processes

Avrachenkova, Konstantin; Cottatellucci, Laura; Maggi, Lorenzo; Mao, Yong-Hua

Statistics and Probability Letters, November 2012

We consider both discrete-time irreducible Markov chains with circulant transition probability matrix View the MathML source and continuous-time irreducible Markov processes with circulant transition rate matrix View the MathML source. In both cases we provide an expression of all the moments of the mixing time. In the discrete case, we prove that all the moments of the mixing time associated with the transition probability matrix View the MathML source are maximum in the interval 0≤α≤1 when α=1/2, where View the MathML source is the transition probability matrix of the time-reversed chain. Similarly, in the continuous case, we show that all the moments of the mixing time associated with the transition rate matrix View the MathML source are also maximum in the interval 0≤α≤1 when α=1/2, where View the MathML source is the time-reversed transition rate matrix.

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Keywords:Circulant Markov process; Maximum mixing time; Moments mixing time
Type:Journal
Language:English
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Department:Mobile Communications
Eurecom ref:3875
Copyright: © Elsevier. Personal use of this material is permitted. The definitive version of this paper was published in Statistics and Probability Letters, November 2012 and is available at : http://dx.doi.org/10.1016/j.spl.2012.11.022
Bibtex: @article{EURECOM+3875, doi = {http://dx.doi.org/10.1016/j.spl.2012.11.022}, year = {2012}, month = {11}, title = {{M}aximum entropy mixing time of circulant {M}arkov processes}, author = {{A}vrachenkova, {K}onstantin and {C}ottatellucci, {L}aura and {M}aggi, {L}orenzo and {M}ao, {Y}ong-{H}ua}, journal = {{S}tatistics and {P}robability {L}etters, {N}ovember 2012}, url = {http://www.eurecom.fr/publication/3875} }
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