Biased random walks on a Galton-Watson tree with leaves

@inproceedings{Gantert2008BiasedRW,
  title={Biased random walks on a Galton-Watson tree with leaves},
  author={Nina Gantert},
  year={2008}
}
We consider a biased random walk Xn on a Galton-Watson tree with leaves in the sub-ballistic regime. We prove that there exists an explicit constant γ = γ(β) ∈ (0, 1), depending on the bias β, such that Xn is of order n . Denoting ∆n the hitting time of level n, we prove that ∆n/n 1/γ is tight. Moreover we show that ∆n/n 1/γ does not converge in law (at least for large values of β). We prove that along the sequences nλ(k) = ⌊λβ⌋, ∆n/n converges to certain infinitely divisible laws. Key tools… CONTINUE READING

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