Local times of subdiffusive biased walks on trees
  Consider a class of null-recurrent randomly biased walks on a super-critical Gaton-Watson tree. We obtain the rates of convergence of the local times and the quenched local probability for the biased walk in the sub-diffusive case. These results are a consequence of a sharp estimate on the return time, whose analysis is driven by a family of concave recursive equations on trees. 
Yueyun Hu
math.PR