M.C. Fujiwara, h,∗ M. Amoretti, d C. Amsler, j G. Bendiscioli, f G. Bonomi, b A. Bouchta, c P. Bowe, a C. Carraro, d M. Charlton, i M. Collier, i M. Doser, c V. Filippini, f K. Fine, c A. Fontana, f R. Funakoshi, h P. Genova, f D. Grögler, j J.S. Hangst, a R.S. Hayano, h H. Higaki, h M.H. Holzscheiter, e W. Joffrain, d L. Jorgensen, i V. Lagomarsino, d R. Landua, c C. Lenz Cesar, g D. Lindelöf,...

We prove an invariance principle for linearly edge reinforced random walks on γ-stable critical Galton-Watson trees, where γ∈(1,2] and the joining x to its parent has rescaled initial weight d(O,x)α some α≤1. This corresponds recurrent regime of weights. then establish fine asymptotics limit process. In transient regime, we also give upper bound walk displacement in discrete setting, showing th...