Stable laws and aging for randomly biased walks on leafless Galton–Watson trees

Consider randomly biased random walks on Galton–Watson trees without leaves, and impose a non-lattice condition on $\log A$, where $A$ is the random bias variable in the model. Stable-law and aging conjecture. This non-lattice condition should allow one to prove stable limit laws, stable subordinators as limiting processes, and the aging property when $\alpha\in(0,1)$. The claim extends the expected trap-model picture to the leafless Galton–Watson-tree model; the source presents it as an open direction.