The speed of a biased walk on a Galton–Watson tree without leaves is monotonic for low values of bias
Abstract We show that for $\lambda\in[0,{m_1}/({1+\sqrt{1-{1}/{m_1}}})]$ , the biased random walk’s speed on a Galton–Watson tree without leaves is strictly decreasing, where $m_1\geq 2$ . Our result extends the monotonic interval of the speed on a Galton–Watson tree.
Authors
- Song He (ORCID: https://orcid.org/0000-0002-2702-8914)
- Longmin Wang (ORCID: https://orcid.org/0000-0002-1741-9401)
- Kainan Xiang
Institutions
- Nankai University (CN)
- Huaiyin Normal University (CN)
- Xiangtan University (CN)
Publication Details
- Journal
- Journal of Applied Probability
- Published
- 2025-03-05
- DOI
- https://doi.org/10.1017/jpr.2024.113
- Citations
- 1
- Primary Topic
- Stochastic processes and statistical mechanics
- Type
- article
- Field-Weighted Citation Impact
- 3.69