Year: 2026
Type: preprint
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. In particular, we give explicit examples of offspring distributions for which the speed is strictly monotone increasing. Additionally, we show that the speed in this model is the limit of the speed of random walks on appropriate locally finite trees.
Source: arXiv (Cornell University)
Author: Nagel, Jan
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7220897776