Geodesic
Time averages and Boltzmann extremals for Markov chains, discrete Liouville equations, and the Kac circular model
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 11, pp. 2063-2074 
S. Z. Adzhiev; V. V. Vedenyapin. Time averages and Boltzmann extremals for Markov chains, discrete Liouville equations, and the Kac circular model. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 11, pp. 2063-2074. http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_11_a9/
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     title = {Time averages and {Boltzmann} extremals for {Markov} chains, discrete {Liouville} equations, and the {Kac} circular model},
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Voir la notice de l'article provenant de la source Math-Net.Ru

Time averages are proved to coincide with Boltzmann extremals for Markov chains, discrete Liouville equations, and their generalizations. A variational principle is proposed for finding stationary solutions in these cases.

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