Biased Random Walk on ${\mathbb{Z}}_{+}$ with Traps of Linearly Increasing Depth

Hua-Ming Wang, Ning Wang

We study a $\lambda$-biased random walk $(X_n{)}_{n\ge 0}$ on the deterministic infinite rooted tree $\mathcal{T}=\{(i,j):i\ge 0,0\le j\le i\}$, whose backbone is $\{(i,0):i\ge 0\}$ and, f…