Geodesic
Stationary distribution of the player rating in the Elo model with one adversary
Diskretnaya Matematika, Tome 26 (2014) no. 4, pp. 3-14.

Voir la notice de l'article provenant de la source Math-Net.Ru

The paper is concerned with the process of fluctuation of the player rating in the Elo model in an infinite series of games with the same adversary. Under some assumptions on the model parameters, this process is shown to have a stationary distribution; its median is found for players of the same skill.
Keywords: models of rating systems, Markov chain, iterated function systems, limit distributions. 
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V. A. Avdeev. Stationary distribution of the player rating in the Elo model with one adversary. Diskretnaya Matematika, Tome 26 (2014) no. 4, pp. 3-14. http://geodesic.mathdoc.fr/item/DM_2014_26_4_a0/

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