Einstein relation for biased random walk on Galton-Watson trees
Annales de l'I.H.P. Probabilités et statistiques, Tome 49 (2013) no. 3, pp. 698-721.

Nous prouvons la relation d'Einstein pour certaines marches aléatoires biaisées sur des arbres de Galton-Watson. Cette formule relie la dérivée de la vitesse à la diffusivité à l'équilibre. Ce travail fournit le premier exemple de preuve de la relation d'Einstein pour une dynamique dans un milieu aléatoire qui comporte des pièges arbitrairement lents.

We prove the Einstein relation, relating the velocity under a small perturbation to the diffusivity in equilibrium, for certain biased random walks on Galton-Watson trees. This provides the first example where the Einstein relation is proved for motion in random media with arbitrarily slow traps.

DOI : 10.1214/12-AIHP486
Classification : 60K37, 60J80, 82C44
Mots-clés : Galton-Watson tree, Einstein relation, spine representation 
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Ben Arous, Gerard; Hu, Yueyun; Olla, Stefano; Zeitouni, Ofer. Einstein relation for biased random walk on Galton-Watson trees. Annales de l'I.H.P. Probabilités et statistiques, Tome 49 (2013) no. 3, pp. 698-721. doi : 10.1214/12-AIHP486. http://www.numdam.org/articles/10.1214/12-AIHP486/

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