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

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.

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.

DOI : https://doi.org/10.1214/12-AIHP486
Classification:  60K37,  60J80,  82C44
Keywords: Galton-Watson tree, Einstein relation, spine representation
@article{AIHPB_2013__49_3_698_0,
     author = {Ben Arous, Gerard and Hu, Yueyun and Olla, Stefano and Zeitouni, Ofer},
     title = {Einstein relation for biased random walk on Galton-Watson trees},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     publisher = {Gauthier-Villars},
     volume = {49},
     number = {3},
     year = {2013},
     pages = {698-721},
     doi = {10.1214/12-AIHP486},
     mrnumber = {3112431},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_2013__49_3_698_0}
}
Einstein relation for biased random walk on Galton-Watson trees. Annales de l'I.H.P. Probabilités et statistiques, Volume 49 (2013) no. 3, pp. 698-721. doi : 10.1214/12-AIHP486. http://www.numdam.org/item/AIHPB_2013__49_3_698_0/

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