Escape regimes of biased random walks on Galton–Watson trees

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 phe...

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Detalles Bibliográficos
Autor principal: Bowditch, Adam
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer Berlin Heidelberg 2017
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6566224/
https://www.ncbi.nlm.nih.gov/pubmed/31258234
http://dx.doi.org/10.1007/s00440-017-0768-y
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author Bowditch, Adam
author_facet Bowditch, Adam
author_sort Bowditch, Adam
collection PubMed
description 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.
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spelling pubmed-65662242019-06-28 Escape regimes of biased random walks on Galton–Watson trees Bowditch, Adam Probab Theory Relat Fields Article 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. Springer Berlin Heidelberg 2017-03-08 2018 /pmc/articles/PMC6566224/ /pubmed/31258234 http://dx.doi.org/10.1007/s00440-017-0768-y Text en © The Author(s) 2017 Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Article
Bowditch, Adam
Escape regimes of biased random walks on Galton–Watson trees
title Escape regimes of biased random walks on Galton–Watson trees
title_full Escape regimes of biased random walks on Galton–Watson trees
title_fullStr Escape regimes of biased random walks on Galton–Watson trees
title_full_unstemmed Escape regimes of biased random walks on Galton–Watson trees
title_short Escape regimes of biased random walks on Galton–Watson trees
title_sort escape regimes of biased random walks on galton–watson trees
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6566224/
https://www.ncbi.nlm.nih.gov/pubmed/31258234
http://dx.doi.org/10.1007/s00440-017-0768-y
work_keys_str_mv AT bowditchadam escaperegimesofbiasedrandomwalksongaltonwatsontrees

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