@article{Song2026, 
author = {He Song and Meng Liu},
title = {Spectral radius of biased random walks on regular trees},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {2},
pages = {4787-4804},
keywords = {biased random walk, spectral radius, continuous},
url = {https://www.sciopen.com/article/10.3934/math.2026195},
doi = {10.3934/math.2026195},
abstract = {For the biased random walk on    d-regular trees, we obtain the spectral radius, first return probability and    n-step transition probability, speed. We prove that the spectral radius depends continuously on the bias parameter and is strictly increasing with respect to it, while the speed remains strictly positive and decreases monotonically as the bias increases.}
}