# Range and critical generations of a random walk on Galton-Watson trees

@article{Andreoletti2015RangeAC, title={Range and critical generations of a random walk on Galton-Watson trees}, author={Pierre Andreoletti and Xinxing Chen}, journal={arXiv: Probability}, year={2015} }

In this paper we consider a random walk in random environment on a tree and focus on the boundary case for the underlying branching potential. We study the range $R\_n$ of this walk up to time $n$ and obtain its correct asymptotic in probability which is of order $n/\log n$. Thisresult is a consequence of the asymptotical behavior of the number of visited sites at generations of order $(\log n)^2$,which turn out to be the most visited generations. Our proof which involves a quenched…

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