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Biased random walk on a locally infinite Galton-Watson tree
Abstract
We propose a new variant of a biased random walk on a Galton-Watson tree, in which some vertices have infinitely many children. These vertices induce a natural regeneration structure, which allows to study differentiability and also monotonicity of the speed of the random walk in the bias parameter. Additionally, we show that the speed in this model is the limit of the speed of random walks on appropriate locally finite trees.
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BibTeX
@misc{nagel2026biased,
title = {{Biased random walk on a locally infinite Galton-Watson tree}},
author = {Jan Nagel},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.08181},
eprint = {2610.08181},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.08181},
}
RIS
TY - UNPB
TI - Biased random walk on a locally infinite Galton-Watson tree
AU - Jan Nagel
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2610.08181
UR - https://arxiv.org/abs/2610.08181
AB - We propose a new variant of a biased random walk on a Galton-Watson tree, in which some vertices have infinitely many children. These vertices induce a natural regeneration structure, which allows to study differentiability and also monotonicity of the speed of the random walk in the bias parameter. Additionally, we show that the speed in this model is the limit of the speed of random walks on appropriate locally finite trees.
ER -