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Biased random walks on a Galton-Watson tree with leaves

Abstract:

We consider a biased random walk $X_n$ on a Galton-Watson tree with leaves in the sub-ballistic regime. We prove that there exists an explicit constant $\gamma= \gamma(\beta) \in (0,1)$, depending on the bias $\beta$, such that $X_n$ is of order $n^{\gamma}$. Denoting $\Delta_n$ the hitting time of level $n$, we prove that $\Delta_n/n^{1/\gamma}$ is tight. Moreover we show that $\Delta_n/n^{1/\gamma}$ does not converge in law (at least for large values of $\beta$). We prove that along the seq...

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Publisher copy:
10.1214/10-AOP620

Authors


Fribergh, A More by this author
Gantert, N More by this author
More by this author
Institution:
University of Oxford
Department:
Oxford, MPLS, Statistics
Journal:
Annals of Probability
Volume:
40
Issue:
1
Pages:
280-338
Publication date:
2007-11-23
DOI:
ISSN:
0091-1798
URN:
uuid:28f4eb50-987f-4590-b2d2-07b0b9341609
Source identifiers:
204289
Local pid:
pubs:204289
Language:
English
Keywords:

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