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.
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}, pages = {698--721}, publisher = {Gauthier-Villars}, volume = {49}, number = {3}, year = {2013}, doi = {10.1214/12-AIHP486}, mrnumber = {3112431}, language = {en}, url = {http://www.numdam.org/articles/10.1214/12-AIHP486/} }
TY - JOUR AU - Ben Arous, Gerard AU - Hu, Yueyun AU - Olla, Stefano AU - Zeitouni, Ofer TI - Einstein relation for biased random walk on Galton-Watson trees JO - Annales de l'I.H.P. Probabilités et statistiques PY - 2013 SP - 698 EP - 721 VL - 49 IS - 3 PB - Gauthier-Villars UR - http://www.numdam.org/articles/10.1214/12-AIHP486/ DO - 10.1214/12-AIHP486 LA - en ID - AIHPB_2013__49_3_698_0 ER -
%0 Journal Article %A Ben Arous, Gerard %A Hu, Yueyun %A Olla, Stefano %A Zeitouni, Ofer %T Einstein relation for biased random walk on Galton-Watson trees %J Annales de l'I.H.P. Probabilités et statistiques %D 2013 %P 698-721 %V 49 %N 3 %I Gauthier-Villars %U http://www.numdam.org/articles/10.1214/12-AIHP486/ %R 10.1214/12-AIHP486 %G en %F AIHPB_2013__49_3_698_0
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, Volume 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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