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Escape regimes of biased random walks on Galton-Watson trees

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Bowditch, Adam (2018) Escape regimes of biased random walks on Galton-Watson trees. Probability Theory and Related Fields, 170 (3-4). pp. 685-768. doi:10.1007/s00440-017-0768-y

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Official URL: https://doi.org/10.1007/s00440-017-0768-y

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Abstract

We study biased random walk on subcritical and supercritical Galton-Watson trees conditioned to survive in the transient, sub-ballistic regime. By considering offspring laws with infinite variance, we extend previously known results for the walk on the supercritical tree and observe new trapping phenomena for the walk on the subcritical tree which, in this case, always yield sub-ballisticity. This is contrary to the walk on the supercritical tree which always has some ballistic phase.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science, Engineering and Medicine > Science > Mathematics
Journal or Publication Title: Probability Theory and Related Fields
Publisher: Springer
ISSN: 0178-8051
Official Date: April 2018
Dates:
DateEvent
April 2018Published
8 March 2017Available
21 February 2017Accepted
Volume: 170
Number: 3-4
Page Range: pp. 685-768
DOI: 10.1007/s00440-017-0768-y
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Open Access

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