Ecole d'ingénieur et centre de recherche en télécommunications

# 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.

 Titre: Maximum entropy mixing time of circulant Markov processes Mots Clés: Circulant Markov process; Maximum mixing time; Moments mixing time Type: Journal Langue: English Ville: Date: Novembre 2012 Département: Systèmes de Communication 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} } Voir aussi: