Abstract

Consider a λ-biased random walk on Galton-Watson trees. It is proved that the speed exists and is bounded above by ( m -λ)=( m +λ), where m is the mean of offsprings. One may further explore the relation between the speed and the offspring distribution. All examples show that the speed is a monotone function of the variance. We confirm this belief by verifying that the recurrent probability, a quantity related to the speed, is a monotone function of the variance of the offspring distribution in some sense, for the fixed m . Some observations are made and some questions are raised.

Full Text
Published version (Free)

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call